#and volume integrals. Line integrals of linear differential forms | Explore Tumblr posts and blogs

fulltestbank · 2 years ago

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Test Bank For Calculus: Early Transcendentals, 12th Edition By Howard Anton

TABLE OF CONTENTS PREFACE vii SUPPLEMENTS ix ACKNOWLEDGMENTS xi THE ROOTS OF CALCULUS xv 1 Limits and Continuity 1 1.1 Limits (An Intuitive Approach) 1 1.2 Computing Limits 13 1.3 Limits at Infinity; End Behavior of a Function 21 1.4 Limits (Discussed More Rigorously) 30 1.5 Continuity 39 1.6 Continuity of Trigonometric Functions 50 1.7 Inverse Trigonometric Functions 55 1.8 Exponential and Logarithmic Functions 62 2 The Derivative 77 2.1 Tangent Lines and Rates of Change 77 2.2 The Derivative Function 87 2.3 Introduction to Techniques of Differentiation 98 2.4 The Product and Quotient Rules 105 2.5 Derivatives of Trigonometric Functions 110 2.6 The Chain Rule 114 3 Topics in Differentiation 124 3.1 Implicit Differentiation 124 3.2 Derivatives of Logarithmic Functions 131 3.3 Derivatives of Exponential and Inverse Trigonometric Functions 136 3.4 Related Rates 142 3.5 Local Linear Approximation; Differentials 149 3.6 L’Hoˆ pital’s Rule; Indeterminate Forms 157 4 The Derivative in Graphing and Applications 169 4.1 Analysis of Functions I: Increase, Decrease, and Concavity 169 4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 180 4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 189 4.4 Absolute Maxima and Minima 200 4.5 Applied Maximum and Minimum Problems 208 4.6 Rectilinear Motion 222 4.7 Newton’s Method 230 4.8 Rolle’s Theorem; Mean-Value Theorem 235 5 Integration 249 5.1 An Overview of the Area Problem 249 5.2 The Indefinite Integral 254 5.3 Integration by Substitution 264 5.4 The Definition of Area as a Limit; Sigma Notation 271 5.5 The Definite Integral 281 5.6 The Fundamental Theorem of Calculus 290 5.7 Rectilinear Motion Revisited Using Integration 302 5.8 Average Value of a Function and its Applications 310 5.9 Evaluating Definite Integrals by Substitution 315 5.10 Logarithmic and Other Functions Defined by Integrals 320 6 Applications of the Definite Integral in Geometry, Science, and Engineering 336 6.1 Area Between Two Curves 336 6.2 Volumes by Slicing; Disks and Washers 344 6.3 Volumes by Cylindrical Shells 354 6.4 Length of a Plane Curve 360 6.5 Area of a Surface of Revolution 365 6.6 Work 370 6.7 Moments, Centers of Gravity, and Centroids 378 6.8 Fluid Pressure and Force 387 6.9 Hyperbolic Functions and Hanging Cables 392 7 Principles of Integral Evaluation 406 7.1 An Overview of Integration Methods 406 7.2 Integration by Parts 409 7.3 Integrating Trigonometric Functions 417 7.4 Trigonometric Substitutions 424 7.5 Integrating Rational Functions by Partial Fractions 430 7.6 Using Computer Algebra Systems and Tables of Integrals 437 7.7 Numerical Integration; Simpson’s Rule 446 7.8 Improper Integrals 458 8 Mathematical Modeling with Differential Equations 471 8.1 Modeling with Differential Equations 471 8.2 Separation of Variables 477 8.3 Slope Fields; Euler’s Method 488 8.4 First-Order Differential Equations and Applications 494 9 Infinite Series 504 9.1 Sequences 504 9.2 Monotone Sequences 513 9.3 Infinite Series 520 9.4 Convergence Tests 528 9.5 The Comparison, Ratio, and Root Tests 534 9.6 Alternating Series; Absolute and Conditional Convergence 539 9.7 Maclaurin and Taylor Polynomials 549 9.8 Maclaurin and Taylor Series; Power Series 559 9.9 Convergence of Taylor Series 567 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 575 10 Parametric and Polar Curves; Conic Sections 588 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 588 10.2 Polar Coordinates 600 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 613 10.4 Conic Sections 622 10.5 Rotation of Axes; Second-Degree Equations 639 10.6 Conic Sections in Polar Coordinates 644 11 Three-dimensional Space; Vector 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 657 11.2 Vectors 663 11.3 Dot Product; Projections 673 11.4 Cross Product 682 11.5 Parametric Equations of Lines 692 11.6 Planes in 3-Space 698 11.7 Quadric Surfaces 705 11.7 Cylindrical and Spherical Coordinates 715 12 Vector-Valued Functions 723 12.1 Introduction to Vector-Valued Functions 723 12.2 Calculus of Vector-Valued Functions 729 12.3 Change of Parameter; Arc Length 738 12.4 Unit Tangent, Normal, and Binormal Vectors 746 12.5 Curvature 751 12.6 Motion Along a Curve 759 12.7 Kepler’s Laws of Planetary Motion 771 13 Partial Derivatives 781 13.1 Functions of Two or More Variables 781 13.2 Limits and Continuity 791 13.3 Partial Derivatives 800 13.4 Differentiability, Differentials, and Local Linearity 812 13.5 The Chain Rule 820 13.6 Directional Derivatives and Gradients 830 13.7 Tangent Planes and Normal Vectors 840 13.8 Maxima and Minima of Functions of Two Variables 845 13.9 Lagrange Multipliers 856 14 Multiple Integrals 925 14.1 Double Integrals 925 14.2 Double Integrals Over Nonrectangular Regions 932 14.3 Double Integrals in Polar Coordinates 941 14.4 Surface Area; Parametric Surfaces 948 14.5 Triple Integrals 961 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 968 14.7 Change of Variables in Multiple Integrals; Jacobians 977 14.8 Centers of Gravity Using Multiple Integrals 989 15 Topics in Vector Calculus 1001 15.1 Vector Fields 1001 15.2 Line Integrals 1010 15.3 Independence of Path; Conservative Vector Fields 1025 15.4 Green’s Theorem 1035 15.5 Surface Integrals 1042 15.6 Applications of Surface Integrals; Flux 1049 15.7 The Divergence Theorem 1058 15.8 Stokes’ Theorem 1067 APPENDIX A A1 APPENDIX B 00 APPENDIX C 00 APPENDIX D 00 APPENDIX E 00 ANSWERS 00 INDEX I1 Read the full article

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coursesforallacademynoida · 5 years ago

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Real And Vector Analysis Online Tutor

Vector Algebra. Operations with vectors. Scalar and vector product of three vectors. Product of four vectors. Reciprocal vectors. Vector Calculus. Scalar-valued functions over the plane and the space. Vector function of a scalar variable: Curves and Paths. Vector fields. Vector differentiation. Directional derivatives, the tangent plane, total differential,…

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foxspain82 · 3 years ago

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10.4 Usubstitution Trig Functionsap Calculus

10.4 U-substitution Trig Functionsap Calculus Answers

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Calculus II, Section 7.4, #67 Integration of Rational Functions by Partial Fractions One method of slowing the growth of an insect population without the use of pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no o spring. Let P represeent. AP Calculus AB Mu Alpha Theta Welcome to AP Calculus AB! Contact me here. Need more review? Browse the Algebra II and Pre-Calculus Tabs. AP ® Calculus AB and BC. COURSE AND EXAM DESCRIPTION. AP COURSE AND EXAM DESCRIPTIONS ARE UPDATED PERIODICALLY. Please visit AP Central. Mathematics 104—Calculus, Part I (4h, 1 CU) Course Description: Brief review of High School Calculus, methods and applications of integration, infinite series, Taylor's theorem, first order ordinary differential equations. Use of symbolic manipulation and graphics software in Calculus. Note: This course uses Maple®.

Math 104: Calculus I – Notes

Section 004 - Spring 2014

10.4 U-substitution Trig Functionsap Calculus Answers

Syllabus

Concept Videos

Skeleton NotesComplete Notes Title More Remainder 10.6, 10.9 Remainder 10.6/10.9 Series Estimation & Remainder Sections 10.8-10.10 Sections 10.8-10.10 Taylor (and Maclaurin) Series Section 10.7 Section 10.7 Power Series Introduction Section 10.6 Section 10.6 Alt. Series Test and Abs. Conv. Conv. Tests Section 10.5 Section 10.5 The Ratio and Root Tests Section 10.4 Section 10.4 The Comparison Tests Section 10.3 Section 10.3 The Integral Test Section 10.2 Section 10.2 Introduction to Series Section 10.1 Section 10.1 Sequences Section 9.2 Section 9.2 Linear Differential Equations Section 7.2 Pt 1Pt 2 Section 7.2 Separable Differential Equations Section 8.8 Section 8.8 Probability and Calculus Odd Ans. Section 8.7 Pt. 1Pt. 2Section 8.7 Improper Integrals L'Hopital Section 8.4 Pt. 1Pt. 2Section 8.4 Partial Fraction Decomposition Section 8.3 Pt. 1Pt. 2Section 8.3 Trig. Substitution Section 8.2 Pt. 1Pt. 2Section 8.2 Integrating Trig. Powers Section 8.1 Pt. 1Pt. 2 Section 8.1 Integration By Parts Section 6.6 Section 6.6 Center of Mass Section 6.4 Section 6.4 Surface Area of Revolution Section 6.3 Section 6.3 Arc Length Section 6.2Section 6.2 Volumes Using Cylindrical Shells Section 6.1 Section 6.1 Volumes Using Cross-Sections disk/washer Review Calc I Review Calc I ReviewLimit, Derivative, and Integral Area b/w CurvesArea b/w Curves Video Example U-substitution Graphs you should know

Print out the skeleton notes before class and bring them to class so that you don't have to write down https://foxspain82.tumblr.com/post/657282647494672384/achievement-unlocked-2watermelon-gaming. Hide paragraph marks in microsoft word for mac. everything said in class. If you miss anything, the complete notes will be posted after class.

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Version #1 The course below follows CollegeBoard's Course and Exam Description. Lessons will begin to appear starting summer 2020. BC Topics are listed, but there will be no lessons available for SY 2020-2021

Unit 0 - Calc Prerequisites (Summer Work) 0.1 Summer Packet

Unit 1 - Limits and Continuity 1.1 Can Change Occur at an Instant? 1.2 Defining Limits and Using Limit Notation 1.3 Estimating Limit Values from Graphs 1.4 Estimating Limit Values from Tables 1.5 Determining Limits Using Algebraic Properties (1.5 includes piecewise functions involving limits) 1.6 Determining Limits Using Algebraic Manipulation 1.7 Selecting Procedures for Determining Limits (1.7 includes rationalization, complex fractions, and absolute value) 1.8 Determining Limits Using the Squeeze Theorem 1.9 Connecting Multiple Representations of Limits Mid-Unit Review - Unit 1 1.10 Exploring Types of Discontinuities 1.11 Defining Continuity at a Point 1.12 Confirming Continuity Over an Interval 1.13 Removing Discontinuities 1.14 Infinite Limits and Vertical Asymptotes 1.15 Limits at Infinity and Horizontal Asymptotes 1.16 Intermediate Value Theorem (IVT) Review - Unit 1

Unit 2 - Differentiation: Definition and Fundamental Properties 2.1 Defining Average and Instantaneous Rate of Change at a Point 2.2 Defining the Derivative of a Function and Using Derivative Notation (2.2 includes equation of the tangent line) 2.3 Estimating Derivatives of a Function at a Point 2.4 Connecting Differentiability and Continuity 2.5 Applying the Power Rule 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple (2.6 includes horizontal tangent lines, equation of the normal line, and differentiability of piecewise) 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x) 2.8 The Product Rule 2.9 The Quotient Rule 2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x) Review - Unit 2

Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions 3.1 The Chain Rule 3.2 Implicit Differentiation 3.3 Differentiating Inverse Functions 3.4 Differentiating Inverse Trigonometric Functions 3.5 Selecting Procedures for Calculating Derivatives 3.6 Calculating Higher-Order Derivatives Review - Unit 3

Unit 4 - Contextual Applications of Differentiation 4.1 Interpreting the Meaning of the Derivative in Context 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 4.3 Rates of Change in Applied Contexts Other Than Motion 4.4 Introduction to Related Rates 4.5 Solving Related Rates Problems 4.6 Approximating Values of a Function Using Local Linearity and Linearization 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms Review - Unit 4

Unit 5 - Analytical Applications of Differentiation 5.1 Using the Mean Value Theorem 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 5.3 Determining Intervals on Which a Function is Increasing or Decreasing 5.4 Using the First Derivative Test to Determine Relative Local Extrema 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 5.6 Determining Concavity of Functions over Their Domains 5.7 Using the Second Derivative Test to Determine Extrema Mid-Unit Review - Unit 5 5.8 Sketching Graphs of Functions and Their Derivatives 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative (5.9 includes a revisit of particle motion and determining if a particle is speeding up/down.) 5.10 Introduction to Optimization Problems 5.11 Solving Optimization Problems 5.12 Exploring Behaviors of Implicit Relations Review - Unit 5

Unit 6 - Integration and Accumulation of Change 6.1 Exploring Accumulation of Change 6.2 Approximating Areas with Riemann Sums 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 6.5 Interpreting the Behavior of Accumulation Functions Involving Area Mid-Unit Review - Unit 6 6.6 Applying Properties of Definite Integrals 6.7 The Fundamental Theorem of Calculus and Definite Integrals 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 6.9 Integrating Using Substitution 6.10 Integrating Functions Using Long Division and Completing the Square 6.11 Integrating Using Integration by Parts (BC topic) 6.12 Integrating Using Linear Partial Fractions (BC topic) 6.13 Evaluating Improper Integrals (BC topic) 6.14 Selecting Techniques for Antidifferentiation Review - Unit 6

Unit 7 - Differential Equations 7.1 Modeling Situations with Differential Equations 7.2 Verifying Solutions for Differential Equations 7.3 Sketching Slope Fields 7.4 Reasoning Using Slope Fields 7.5 Euler's Method (BC topic) 7.6 General Solutions Using Separation of Variables 7.7 Particular Solutions using Initial Conditions and Separation of Variables 7.8 Exponential Models with Differential Equations 7.9 Logistic Models with Differential Equations (BC topic) Review - Unit 7

Unit 8 - Applications of Integration 8.1 Average Value of a Function on an Interval 8.2 Position, Velocity, and Acceleration Using Integrals 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 8.4 Area Between Curves (with respect to x) 8.5 Area Between Curves (with respect to y) 8.6 Area Between Curves - More than Two Intersections Mid-Unit Review - Unit 8 8.7 Cross Sections: Squares and Rectangles 8.8 Cross Sections: Triangles and Semicircles 8.9 Disc Method: Revolving Around the x- or y- Axis 8.10 Disc Method: Revolving Around Other Axes 8.11 Washer Method: Revolving Around the x- or y- Axis 8.12 Washer Method: Revolving Around Other Axes 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC topic) Review - Unit 8

Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC topics) 9.1 Defining and Differentiating Parametric Equations 9.2 Second Derivatives of Parametric Equations 9.3 Arc Lengths of Curves (Parametric Equations) 9.4 Defining and Differentiating Vector-Valued Functions 9.5 Integrating Vector-Valued Functions 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions 9.7 Defining Polar Coordinates and Differentiating in Polar Form 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 9.9 Finding the Area of the Region Bounded by Two Polar Curves Review - Unit 9

Unit 10 - Infinite Sequences and Series (BC topics) 10.1 Defining Convergent and Divergent Infinite Series 10.2 Working with Geometric Series 10.3 The nth Term Test for Divergence 10.4 Integral Test for Convergence 10.5 Harmonic Series and p-Series 10.6 Comparison Tests for Convergence 10.7 Alternating Series Test for Convergence 10.8 Ratio Test for Convergence 10.9 Determining Absolute or Conditional Convergence 10.10 Alternating Series Error Bound 10.11 Finding Taylor Polynomial Approximations of Functions 10.12 Lagrange Error Bound 10.13 Radius and Interval of Convergence of Power Series 10.14 Finding Taylor Maclaurin Series for a Function 10.15 Representing Functions as a Power Series Review - Unit 8

Version #2 The course below covers all topics for the AP Calculus AB exam, but was built for a 90-minute class that meets every other day. Lessons and packets are longer because they cover more material.

Unit 0 - Calc Prerequisites (Summer Work) 0.1 Things to Know for Calc 0.2 Summer Packet 0.3 Calculator Skillz

Unit 1 - Limits 1.1 Limits Graphically 1.2 Limits Analytically 1.3 Asymptotes 1.4 Continuity Review - Unit 1

Unit 2 - The Derivative 2.1 Average Rate of Change 2.2 Definition of the Derivative 2.3 Differentiability (Calculator Required) Review - Unit 2

Unit 3 - Basic Differentiation 3.1 Power Rule 3.2 Product and Quotient Rules 3.3 Velocity and other Rates of Change 3.4 Chain Rule 3.5 Trig Derivatives Review - Unit 3

Unit 4 - More Deriviatvies 4.1 Derivatives of Exp. and Logs 4.2 Inverse Trig Derivatives 4.3 L'Hopital's Rule Review - Unit 4

Unit 5 - Curve Sketching 5.1 Extrema on an Interval 5.2 First Derivative Test 5.3 Second Derivative Test Review - Unit 5

Unit 6 - Implicit Differentiation 6.1 Implicit Differentiation 6.2 Related Rates 6.3 Optimization Review - Unit 6

Unit 7 - Approximation Methods 7.1 Rectangular Approximation Method 7.2 Trapezoidal Approximation Method Review - Unit 7

Unit 8 - Integration 8.1 Definite Integral 8.2 Fundamental Theorem of Calculus (part 1) 8.3 Antiderivatives (and specific solutions) Review - Unit 8

Unit 9 - The 2nd Fundamental Theorem of Calculus 9.1 The 2nd FTC 9.2 Trig Integrals 9.3 Average Value (of a function) 9.4 Net Change Review - Unit 9

Unit 10 - More Integrals 10.1 Slope Fields 10.2 u-Substitution (indefinite integrals) 10.3 u-Substitution (definite integrals) 10.4 Separation of Variables Review - Unit 10

Unit 11 - Area and Volume 11.1 Area Between Two Curves 11.2 Volume - Disc Method 11.3 Volume - Washer Method 11.4 Perpendicular Cross Sections Review - Unit 11

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sunblog29 · 3 years ago

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Quantum Qhm7468-2a Usb Gamepad Driver

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ba3up891186 · 4 years ago

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RESILIENT CITIES UNIT OUTLINE

1. The Future of our Towns and Cities

Cities grow and transform to accommodate the ever-changing needs of people. Architects are asked to design buildings and cities capable of meeting such needs and enhance the well-being of the many diverse urban communities and groups, and at the same time safeguard the environment. That is why today more than ever, cities must be designed as inclusive, resilient and open systems.

Creating “Inclusive, safe, resilient and sustainable” cities is an imperative for future cities development. The key questions architects and urban designers need to answer are “What means resilience on an urban level?” and “How can we contribute to create a resilient city?”.

A resilient city is a city that in the processes of development can cope with critical both chronic and traumatic problems. A city that is sustainable both ecologically and socially. A city that is in ecological balance with the natural environment and includes all citizens, avoiding marginalization of weaker social groups. The concept of the resilient city has to be understood as a complex phenomenon that involves multiple social, economic, ecological and spatial factors. The interdependency of these elements determines different levels of urban resilience.

Many historic cities have a great potential for modernization but because of their historical heritage, it is particularly difficult to adapt to new scenarios of life without losing important architectural and urban features. Yet, a constantly increasing urban population poses the problem of retrofitting the city and expanding its capacity. Since in a tight urban fabric large sites are not available to accommodate the many complementary new uses needed, an ‘acupuncture’ approach might be needed, in which many small interventions connected and coordinated yield great benefits. In other words, buildings and open spaces designed to meet a programme are dispersed but connected over a wider area of the city, thus creating a rich and diverse environment that improves the wider urban context.

2. Where We Will Work

The project is set around Peckham town centre, London. Peckham town centre is the area surrounding Rye Lane, an incredibly dense and lively multicultural street. This area is part of the Peckham and Nunhead action area, within the London Borough of Southwark.

“Peckham town centre, which is the commercial heart of Peckham and adjacent areas. This is primarily composed of three main streets - Rye Lane, Peckham High Street and Peckham Hill Street - and a few adjacent areas. The main streets are lined with retail shops and a variety of businesses: see the red-lined streets on the map; click to enlarge. Many people live in the town centre above and among the businesses, and the commercial premises back mostly directly onto the residential areas. The town centre is therefore integrated tightly with the residential area, and its impact also spreads widely throughout a wider geographical area because of its physical, social and economic effects” (http://www.peckhamvision.org).

The character of Peckham town centre area is very different to the surroundings. The differences in scale, grain and land use between the town centre and the wider area is very marked.These are retail and light industrial uses, alongside important community and leisure facilities including the cinema, the library and Peckham Pulse leisure centre. There are also some homes within the core action area, mostly flats along Queens Road just outside the town centre boundary.

In contrast the wider area is predominantly residential along with important local shopping parades, providing for residents’ day to day needs. There are a range of different housing types including large amounts of council housing and Victorian terraced housing. Towards the south there are more semi-detached and detached homes with gardens. There is also a lot of open space within the wider action area, especially within the Nunhead, Peckham Rye and Honor Oak character areas.

(Peckham and Nunhead Area Action Plan, 2014)

Peckham town centre is:

● A lively town centre providing a range of daytime and night time activities on Rye Lane including a Library, a Leisure Centre and many independent retailers which specialise in West African goods. Bellenden Road is a quieter alternative. Much of the town centre activity spills over to busy side streets;

● An area with a burgeoning sector of small and medium enterprises, many of which are creative industries;

● An area of heritage value, particularly in the conservation areas with many interesting Victorian, Edwardian and inter-war buildings, including Peckham Rye Station, and the Baptist church with the former Jones and Higgins department store at the heart of Peckham town centre. Outside designated conservation area the historic residential layout of much of the area remains intact;

● A place for sports and activities with local parks which support leisure and cultural activities. Examples include Peckham Square, Peckham Rye Station Square, Peckham Rye Common and the Surrey Canal Walk connecting Peckham to Burgess Park and beyond;

● Accessible by rail from central London and wider London with stations at Peckham Rye and Queen’s Road along with many bus routes. Peckham is very accessible for walking and cycling.

(New Southwark Plan Preferred Option - Area Visions And Site Allocations - 2017)

Peckham town center is one of the most diverse areas in London and in the UK. “On a kilometre stretch of street on Rye Lane in Peckham, South London, 199 formal units of retail are tightly packed adjacent to one another, forming a dense, linear assemblage of economic and cultural diversity. The majority of these units are occupied by independent proprietors, aligning among them over twenty countries of origin: Afghanistan, England, Eritrea, Ghana, India, Ireland, Iran, Iraq, Jamaica, Pakistan, Kashmir, Kenya, Nepal, Nigeria, Somalia, Sri Lanka, Tanzania, Uganda, Vietnam and Yemen” (Hall S., Super-diverse street: a ‘trans-ethnography’ across migrant localities, 2013).

This could be defined as a “super-diverse” environment,. The term superdiversity is used to refer to some current levels of population diversity that are significantly higher than before. Vertovec, who coined the term in 2007, argues superdiversity in Britain "is distinguished by a dynamic interplay of variables among an increased number of new, small and scattered, multiple-origin, transnationally connected, socio-economically differentiated and legally stratified immigrants who have arrived over the last decade". It denotes increased diversity not only between immigrant and ethnic minority groups, but also within them. It has also been called the "diversification of diversity". (https://en.wikipedia.org/wiki/Superdiversity)

3. The Problem to Resolve

The current population of The Lane Ward (Southwark) is 16350 people. According to Southwark Council projections, in the next 20 years there will be approximately a 30% population increase. Students will have to design an urban proposal that addresses this trend of population growth and aim to accommodate approximately 5000 people by 2040.

Design proposals have to address the contemporary environmental agenda and envision future cities that are sustainable, resilient and aim to reduce the human carbon footprint a series of key factors such as food, transportation, and household energy. The design proposals need also to develop some considerations of the key aspects of private and social life, such as goods and economic exchange, spiritual rituals, entertainment and healthy living: Sleeping, eating, gathering, praying, buying, selling, studying, exercising, leisuring.

Considering that the average household size in Southwark is 2.15 people, this means that this future city (if of the size of The Lane Ward) will have to provide approximately 2300 new residential units. Just for the purpose of volumetric comparison, Trellik Tower in London < https://en.wikipedia.org/wiki/Trellick_Tower > accommodates 217 residential units (on 31 floors). This volume accommodates only the residential use, without all the other uses that are needed in a city.

What is the vision of Peckham 2040 as a sustainable and liveable urban environment?

The calculations above refer to an area equivalent to the Lane Ward but students are allowed to pick a smaller area for the proposed design, making some reflection on average urban densities. This will indeed reduce the overall quantities of new inhabitants and flat requirement but population growth rate remains the same and so the resulting density for the proposed scenario.

#design #brief #architecture

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mamtajuyal1986 · 5 years ago

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IIT JAM 2020 Mathematics (MA) Syllabus | IIT JAM 2020 Mathematics (MA) Exam Pattern

IIT JAM 2020 Mathematics (MA) Syllabus | IIT JAM 2020 Mathematics (MA) Exam Pattern Mathematics (MA): The syllabus is a very important aspect while preparing for the examination. Therefore it is advised to all the appearing candidates that they should go through the Mathematics (MA) syllabus properly before preparing for the examination. Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences,subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms - comparison test, ratio test, root test; Leibniz test for convergence of alternating series. Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle's Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima and minima. Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima and minima. Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y), Bernoulli,s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation. Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems. Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups. Linear Algebra: Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix,determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices,Cayley-Hamilton theorem. Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor,s series, radius and interval of convergence, term-wise differentiation and integration of power series. Related Articles: IIT JAM 2020 Syllabus Biotechnology (BT) Syllabus Biological Sciences (BL) Syllabus Chemistry (CY) Syllabus Geology (GG) Syllabus Mathematics (MA) Syllabus Mathematical Statistics (MS) Syllabus Physics (PH) Syllabus Read the full article

#IITJAM2020 #IITJAM2020MASyllabus #IITJAM2020Syllabus

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toppersexam · 4 years ago

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NDA 2020 Age Limit, Syllabus, Online Free Mock Test, MCQ, Books

NDA 2020 Age Limit, Syllabus, Online Free Mock Test, MCQ, Books NDA (II) 2020 Rejected applicants list has been published due to non-payment of exam fee. Admit Card is releasing soon. The exam will be conducted by Union Public Service Commission (UPSC). UPSC NDA entrance exam is a gateway for the aspirants who want to make their career in Indian Army, Navy and Air Force. NDA Age Limit It should be clearly noted that only unmarried male candidates, who are not born earlier than July 2, 2001 and not later than July 1, 2004 are eligible to appear for NDA 1 Exam. For NDA 2 2020, candidates must be born between January 2, 2002 and January 1, 2005.

NDA Free Online Mock Test Crack NDA Recruitment exam with the help of online mock test Series or Free Mock Test. Every Sample Paper in NDA Exam has a designated weightage so do not miss out any Paper. Prepare and Practice Mock for NDA exam and check your test scores. You can get an experience by doing the Free Online Test or Sample Paper of NDA Exam. Free Mock Test will help you to analysis your performance in the Examination. NDA Free Online Mock Test : Available Now NDA MCQs Buy the question bank or online quiz of NDA Exam Going through the NDA Exam Question Bank is a must for aspirants to both understand the exam structure as well as be well prepared to attempt the exam. The first step towards both preparation as well as revision is to practice from NDA Exam with the help of Question Bank or Online quiz. We will provide you the questions with detailed answer. NDA MCQs : Available Now NDA 2020 Syllabus Paper-1 : Mathematics Algebra 1. relation, Logarithms and their applications. 2. equivalence relation. 3. Representation of real numbers on a line. 4. Complex numbers—basic properties, 5. modulus, argument, Binomial theorem and its applications 6. cube roots of unity. 7. Solution of linear inequations of two variables by graphs. 8. Binary system of numbers. 9. Conversion of a number in decimal system to binary system and vice-versa. 10. Arithmetic, Permutation and Combination. 11. Geometric and Harmonic progressions. 12. Quadratic equations with real coefficients. 13. Solution of linear inequations of two variables by graphs. Matrices and Determinants 1. Types of matrices, Adjoint and inverse of a square matrix, 2. operations on matrices.basic properties of determinants. 3. Determinant of a matrix, 4. Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method. Trigonometry 1. Angles and their measures in degrees and in radians. 2. Trigonometrical ratios. 3. Trigonometric identities Sum and difference formulae. 4. Multiple and Sub-multiple angles. 5. Inverse trigonometric functions. 6. Applications-Height and distance, 7. properties of triangles. Analytical Geometry of Two and Three Dimensions 1. Rectangular Cartesian Coordinate system. 2. Distance formula.Direction Cosines and direction ratios. 3. Equation of a line in various forms. 4. Angle between two lines. 5. Distance of a point from a line. 6. Equation of a circle in standard and in general form. 7. Standard forms of parabola,Equation of a sphere. 8. ellipse and hyperbola.Equation two points. 9. Eccentricity and axis of a conic. 10. Point in a three dimensional space, 11. distance between two points. 12. Direction Cosines and direction ratios. 15. Equation of a plane and a line in various forms. 16. Angle between two lines and angle between two planes. Differential Calculus 1. Concept of a real valued function–domain, 2. range and graph of a function. 3. Composite functions, Derivatives of sum, 4. one to one, Increasing and decreasing functions. 5. onto and inverse functions. 6. Notion of limit, Second order derivatives. 7. Standard limits—examples. 8. Continuity of functions - examples, 9. algebraic operations on continuous functions. 10. Derivative of function at a point, 11. geometrical and physical interpretation of a derivative-application. 12. derivative of a function with respect to another function, 13. product and quotient of functions, 15. derivative of a composite function. 16. Application of derivatives in problems of maxima and minima Integral Calculus and Differential Equations 1. Integration as inverse of differentiation, 2. integration by substitution and by parts, 3. standard integrals involving algebraic expressions, 4. trigonometric, Application in problems of growth and decay. 5. exponential and hyperbolic functions. 6. Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications. 7. Definition of order and degree of a differential equation, 8. formation of a differential equation by examples. 9. General and particular solution of a differential equations, 10. solution of first order and first degree differential equations of various types—examples. Victor Algebra 1. Vectors in two and three dimensions, 2. magnitude and direction of a vector. 3. Unit and null vectors, addition of vectors, 4. Applications—work done by a force and moment of a force and in geometrical problems. 5. scalar multiplication of a vector, 6. scalar product or dot product of two vectors. 7. Vector product or cross product of two vectors. Statistics and Probability 1. Statistics: Classification of data, 2. Frequency distribution, Conditional probability, 3. cumulative frequency distribution - examples. 4. Graphical representation - Histogram, 5. Pie Chart, frequency polygon—examples. Measures of Central tendency— Mean, median and mode. 6. Variance and standard deviation determination and comparison. 7. Correlation and regression.Probability: Random experiment, 8. outcomes and associated sample space, events, 9. mutually exclusive and exhaustive events, impossible and certain events. 10. Union and Intersection of events. Complementary, 11. elementary and composite events. Definition of probability—classical and statistical—examples. 12 .Elementary theorems on probability—simple problems. 13 .Bayes’ theorem—simple problems. Random variable as function on a sample space. 14 .Binomial distribution, 15. examples of random experiments giving rise to Binominal distribution. Paper-2 : General Ability Test English 1. Grammar and usage, vocabulary, comprehension General Knowledge Physics 1. Physical Properties and States of Matter, 2. Mass, Weight, Volume, 3. Density and Specific Gravity, Principle of Archimedes, 4. Pressure Barometer. Motion of objects, 5. Velocity and Acceleration, Newton’s Laws of Motion, 6. Force and Momentum, Parallelogram of Forces, 7. Stability and Equilibrium of bodies, Gravitation, 8. elementary ideas of work, Power and Energy. 9. Effects of Heat, Measurement of Temperature and Heat, 10. change of State and Latent Heat, Modes of transference of Heat. 11. Sound waves and their properties, Simple musical instruments. 12. Rectilinear propagation of Light, Reflection and refraction. 13. Spherical mirrors and Lenses, Human Eye. 14. Natural and Artificial Magnets, Properties of a Magnet, 15. Earth as a Magnet.Static and Current Electricity, 16. conductors and Non-conductors,Ohm’s Law, 17. Simple Electrical Circuits, Heating, 18. Lighting and Magnetic effects of Current, 19. Measurement of Electrical Power, 20. Primary and Secondary Cells, Use of X-Rays. 21. General Principles in the working of the following: 22. Simple Pendulum, Simple Pulleys, Siphon, 23. Levers, Balloon,Pumps, Hydrometer, 24. Pressure Cooker, Thermos Flask, Gramophone, 25. Telegraphs, Telephone, Periscope, Telescope, 26. Microscope, Mariner’s Compass; 27. Lightening Conductors, Safety Fuses Chemistry 1. Physical and Chemical changes. 2. Elements, Carbon - different forms. 3. Mixtures and Compounds, 4. Symbols, Fertilizers—Natural and Artificial. 5. Formulae and simple Chemical Equations, 6. Law of Chemical Combination (excluding problems). 7. Properties of Air and Water. 8. Preparation and Properties of Hydrogen, 9. Oxygen,Glass, Ink, Paper, Cement, 10. Nitrogen and Carbondioxide, 11. Oxidation and Reduction. 12. Acids, bases and salts. 13. Material used in the preparation of substances like Soap, 14. Paints, Safety Matches and Gun-Powder. 15. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency. General Science 1. Difference between the living and non-living. Basis of Life—Cells, 2. Protoplasms and Tissues. Growth and Reproduction in Plants and Animals. 3. Elementary knowledge of Human Body and its important organs. 4. Common Epidemics, their causes and prevention. 5. Food—Source of Energy for man. Constituents of food, 6. Balanced Diet. The Solar System—Meteors and Comets, 7. Eclipses. Achievements of Eminent Scientists. History Freedom Movement 1. A broad survey of Indian History, with emphasis on Culture and Civilisation. 2. Freedom Movement in India. Elementary study of Indian Constitution and Administration. 3. Elementary knowledge of Five Year Plans of India. 4. Panchayati Raj, Co-operatives and Community Development. 5. Bhoodan, Sarvodaya, National Integration and Welfare State, 6. Basic Teachings of Mahatma Gandhi.Exploration and Discovery; 7. Forces shaping the modern world; Renaissance, 8. War of American Independence. French Revolution, 9. Industrial Revolution and Russian Revolution. 10. Impact of Science and Technology on Society. 11. Concept of one World, United Nations, Panchsheel, 12. Democracy, Socialism and Communism. Role of India in the present world. Geography 1. The Earth, its shape and size. Lattitudes and Longitudes, 2. Concept of time. International Date Line. . 3. Origin of Earth. Rocks and their classification; 4. Weathering-Mechanical and Chemical, 5. Earthquakes and Volcanoes.Movements of Earth and their effects. 6. Ocean Currents and Tides Atmosphere and its composition; 7. Temperature and Atmospheric Pressure, 8. Planetary Winds, Cyclones and Anti-cyclones; 9. Humidity; Condensation and Precipitation; 10. Types of Climate, Major Natural regions of the World. 11. Regional Geography of India—Climate, Natural vegetation. 12. Mineral and Power resources; 13. location and distribution of agricultural and Industrial activities. 14. Important Sea ports and main sea, 15. land and air routes of India. Main items of Imports and Exports of India. Current Events 1. Knowledge of Important events that have happened in India in the recent years. 2. Current important world events. 3. Prominent personalities—both Indian and International including those connected with cultural activities and sports. NDA Exam Pattern 2020 Negative Marking : Mathematics : 0.83 General Abilities : 1.33 PaperSubjectNo. of QuestionMarksDuration Paper -1 Mathematics120300150 Minutes Paper - IIGeneral Ability Test (English & General Knowledge)

#NDA NDA2020 NDAExam FreeTestSeries QuestionsBank NDASyllabus OnlineTestSeries OnlineMockTest ImportantQuestionPaper ImportantQuestion Import

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glitterypeacesong · 5 years ago

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IIT JAM Mathematics Syllabus

Always remember that before starting the preparation for any exam, must check the complete Syllabus, its essential.

This will help you in making strategy for preparation.

Check out the JAM Mathematics Syllabus here.

You can also check important topics, best books for preparation, tips and get free pdf of previous papers from HERE – IIT JAM Mathematics.

IIT-JAM Mathematics Syllabus

Sequences and Series of Real Numbers: Sequences and series of real numbers, Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibnitz test for convergence of alternating series.

Functions of One Variable: limit, continuity, differentiation, Rolle’s Theorem, Mean value theorem. Taylor's theorem. Maxima and minima.

Functions of Two Real Variables: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler’s theorem.

Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli’s equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy-Euler equation.

Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.

Group Theory: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups (only group theory).

Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skew-symmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor’s and Maclaurin’s, domain of convergence, term-wise differentiation and integration of power series.

Thank You!!

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fulltestbank · 2 years ago

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Test Bank For Calculus: Early Transcendentals Single Variable, 12th Edition by Howard Anton

TABLE OF CONTENTS PREFACE vii SUPPLEMENTS ix ACKNOWLEDGMENTS xi THE ROOTS OF CALCULUS xv 1 Limits and Continuity 1 1.1 Limits (An Intuitive Approach) 1 1.2 Computing Limits 13 1.3 Limits at Infinity; End Behavior of a Function 21 1.4 Limits (Discussed More Rigorously) 30 1.5 Continuity 39 1.6 Continuity of Trigonometric Functions 50 1.7 Inverse Trigonometric Functions 55 1.8 Exponential and Logarithmic Functions 62 2 The Derivative 77 2.1 Tangent Lines and Rates of Change 77 2.2 The Derivative Function 87 2.3 Introduction to Techniques of Differentiation 98 2.4 The Product and Quotient Rules 105 2.5 Derivatives of Trigonometric Functions 110 2.6 The Chain Rule 114 3 Topics in Differentiation 124 3.1 Implicit Differentiation 124 3.2 Derivatives of Logarithmic Functions 131 3.3 Derivatives of Exponential and Inverse Trigonometric Functions 136 3.4 Related Rates 142 3.5 Local Linear Approximation; Differentials 149 3.6 L'Hôpital's Rule; Indeterminate Forms 157 4 The Derivative in Graphing and Applications 169 4.1 Analysis of Functions I: Increase, Decrease, and Concavity 169 4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 180 4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 189 4.4 Absolute Maxima and Minima 200 4.5 Applied Maximum and Minimum Problems 208 4.6 Rectilinear Motion 222 4.7 Newton's Method 230 4.8 Rolle's Theorem; Mean-Value Theorem 235 5 Integration 249 5.1 An Overview of the Area Problem 249 5.2 The Indefinite Integral 254 5.3 Integration by Substitution 264 5.4 The Definition of Area as a Limit; Sigma Notation 271 5.5 The Definite Integral 281 5.6 The Fundamental Theorem of Calculus 290 5.7 Rectilinear Motion Revisited Using Integration 302 5.8 Average Value of a Function and Its Applications 310 5.9 Evaluating Definite Integrals by Substitution 315 5.10 Logarithmic and Other Functions Defined by Integrals 320 6 Applications of the Definite Integral in Geometry, Science, and Engineering 336 6.1 Area Between Two Curves 336 6.2 Volumes by Slicing; Disks and Washers 344 6.3 Volumes by Cylindrical Shells 354 6.4 Length of a Plane Curve 360 6.5 Area of a Surface of Revolution 365 6.6 Work 370 6.7 Moments, Centers of Gravity, and Centroids 378 6.8 Fluid Pressure and Force 387 6.9 Hyperbolic Functions and Hanging Cables 392 7 Principles of Integral Evaluation 406 7.1 An Overview of Integration Methods 406 7.2 Integration by Parts 409 7.3 Integrating Trigonometric Functions 417 7.4 Trigonometric Substitutions 424 7.5 Integrating Rational Functions by Partial Fractions 430 7.6 Using Computer Algebra Systems and Tables of Integrals 437 7.7 Numerical Integration; Simpson's Rule 446 7.8 Improper Integrals 458 8 Mathematical Modeling with Differential Equations 471 8.1 Modeling with Differential Equations 471 8.2 Separation of Variables 477 8.3 Slope Fields; Euler's Method 488 8.4 First-Order Differential Equations and Applications 494 9 Infinite Series 504 9.1 Sequences 504 9.2 Monotone Sequences 513 9.3 Infinite Series 520 9.4 Convergence Tests 528 9.5 The Comparison, Ratio, and Root Tests 534 9.6 Alternating Series; Absolute and Conditional Convergence 540 9.7 Maclaurin and Taylor Polynomials 549 9.8 Maclaurin and Taylor Series; Power Series 559 9.9 Convergence of Taylor Series 567 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 575 10 Parametric and Polar Curves; Conic Sections 588 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 588 10.2 Polar Coordinates 600 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 613 10.4 Conic Sections 622 10.5 Rotation of Axes; Second-Degree Equations 639 10.6 Conic Sections in Polar Coordinates 644 A Appendices A Trigonometry Review (Summary) App-1 B Functions (Summary) App-8 C New Functions From Old (Summary) App-11 D Families of Functions (Summary) App-16 E Inverse Functions (Summary) App-23 READY REFERENCE RR-1 ANSWERS TO ODD-NUMBERED EXERCISES Ans-1 INDEX Ind-1 Web Appendices (online only) Available in WileyPLUS A Trigonometry Review B Functions C New Functions From Old D Families of Functions E Inverse Functions F Real Numbers, Intervals, and Inequalities G Absolute Value H Coordinate Planes, Lines, and Linear Functions I Distance, Circles, and Quadratic Equations J Solving Polynomial Equations K Graphing Functions Using Calculators and Computer Algebra Systems L Selected Proofs M Early Parametric Equations Option N Mathematical Models O The Discriminant P Second-Order Linear Homogeneous Differential Equations Chapter Web Projects: Expanding the Calculus Horizon (online only) Available in WileyPLUS Robotics -- Chapter 2 Railroad Design -- Chapter 7 Iteration and Dynamical Systems -- Chapter 9 Comet Collision -- Chapter 10 Read the full article

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mathematicianadda · 6 years ago

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Returning to CSE maths 4 years after High School

I know this subreddit says that questions about "learning maths" should be on r/learnmath but I feel that my question is a little more focused (not just about...wanting book or resources) and could be answered here. Nevertheless, I will be posting this on there too.

This is a long one... bear with me. If you will.

I am going into the second year of a Computer Science degree and we have a course called "Engineering Mathematics" (ME3) in the next semester.

I graduated high school a WHILE ago and honestly need a little brushing up before I start learning ME3. But I don't have the time to go through all the maths topics we had then in all the 4 years. I was wondering if someone could help me decide what I should revisit and revise before going on to ME3.

Course Content of ME3

------------------------------------

1 - Linear Differential Equations (LDE)

\- LDE of nth order with constant coefficients \- Method of variation of parameters \- Cauchy's & Legendre's LDE \- Simultaneous & Symmetric Simultaneous DE \- Modelling of Electric Circuits

2 - Transforms

\- Fouriers Transform \- Complex exponential form Fourier series \- Fourier Integral Theorem \- Fourier Sine & Cosine Integrals \- Fourier Sine & Cosine transforms & their inverses \- Z Transform (ZT) \- Standard Properties \- ZT of standard sequences & their inverse

3 - Statistics

\- Measures of Central tendency \- Standard deviation, \- Coefficient of variation, \- Moments, Skewness and Kurtosis \- Curve fitting: fitting of straight line \- Parabola and Related curves \- Correlation and Regression \- Reliability of Regression Estimates.

4 - Probability and Probability Distributions

\- Probability, Theorems on Probability \- Bayes Theorem, \- Random variables, \- Mathematical Expectation \- Probability density function \- Probability distributions: Binomial, Poisson, Normal and Hypergometric \- Test of Hypothesis: Chi-Square test, t-distribution

5 - Vector Calculus

\- Vector differentiation \- Gradient, Divergence and Curl \- Directional derivative \- Solenoid and Irrigational fields \- Vector identities. Line, Surface and Volume integrals \- Green‘s Lemma, Gauss‘s Divergence theorem and Stoke‘s theorem

6 - Complex Variables

\- Functions of Complex variables \- Analytic functions \- Cauchy-Riemann equations \- Conformal mapping \- Bilinear transformation \- Cauchy‘s integral theorem & Cauchy‘s integral formula, \- Laurent‘s series, and Residue theorem

-------------------------------------------------------------------------------------------

Overview of roughly what all we had in the years of High School, a little out of order because I am summarizing all 4 years of Math books.

Real Numbers

\- Laws of Exponents for Real Numbers \- Euclid’s Division Lemma \- Fundamental Theorem of Arithmetic

Polynomials

\- Polynomials in One Variable \- Zeroes of a Polynomia, Remaider Theorem, Factorization of Polynomials \- Relationship between Zeroes and Coefficients of a Polynomial \- Division Algorithm for Polynomials

Pair of Linear Equations in Two variables

\- Linear Equations \- Solution of a Linear Equation \- Pair of Linear Equations in Two Variables \- Graphical Method of Solution of a Pair of Linear Equations \- Substitution Method, Elimination Method & Cross-Multiplication Method

Principles of Mathematical Induction

Complex Numbers

\- Modulus and the Conjugate \- Argand Plane and Polar Representation

Quadratic Equations

\- Factorisation & Completing the Square, Roots of Equations.

Sets----------

\- Sets: Empty, Finite, Infinite, Equal, Subsets, Power Set, Universal Set. \- Venn Diagrams \- Union, Intersection & Complement of a Set

Permutations and Combinations

Binomial Theorem

\- Binomial Theorem for Positive Integral Indices \- General and Middle Terms

Sequences and Series

\- Sequences & Series \- Arithmetic Progressions \- nth Term of an AP, Sum of n terms of an AP \- Geometric Progression \- Relationship Between Arithematic Mean and Geometric Mean

Matrices

\- Types & Operations \- Transpose \- Symmetric and Skew Symmetric Matrices \- Transformation \- Invertible Matrices

Determinants

\- Properties of Determinants \- Area of a Triangle \- Minors and Cofactors \- Adjoint and Inverse of a Matrix \- Applications of Determinants and Matrices

Relations and Functions

\- Cartesian Product of Sets \- Relations & Functions \- Composition of Functions and Invertible Function \- Binary Operations

Limits and Derivatives

\- Limits, Derivatives \- Limits of Trigonometric Functions \- Applications: Rate of Change of Quantities, Increasing and Decreasing Functions

Tangents and Normals, Approximations & Maxima and Minima

Continuity and Differentiability

\- Exponential and Logarithmic Functions \- Logarithmic Differentiation \- Derivatives of Functions in Parametric Forms \- Second Order Derivative \- Mean Value Theorem

Integrals

\- Inverse Process of Differentiation \- Methods of Integration \- Integration by Partial Fractions & by Parts \- Definite Integral \- Fundamental Theorem of Calculus \- Definite Integrals by Substitution \- Properties of Definite Integrals \- Applications: Area under Simple Curves, Area between Two Curves

Differential Equations

\- Basic Concepts \- General and Particular Solutions of Differential Equation \- Differential Equation whose General Solution is given \- Methods of Solving First order, First Degree Differential Equations

Vector Algebra

\- Types of Vectors \- Addition of Vectors, Multiplication of a Vector by a Scalar \- Product of Two Vectors

Linear Programming

Statistics

\- Graphical Representation \- Distribution. Mean, Mode & Median \- Measures of Dispersion, Range, Mean Deviation \- Variance and Standard Deviation

Probability

\- Random Experiments, Events, Axiomatic Approach to Probability \- Conditional Probability , Multiplication Theorem, Independent Events \- Bayes' Theorem \- Random Variables and their Probability Distributions \- Bernoulli Trials and Binomial Distribution

------------------------------------------------------------------------------

Euclids's Geometry

Properties of Lines, Angles, Circles, Triangles, Quadrilaterals, Parallelograms (Too easy to worry about)

Some chapters about Areas & Volumes of Quadrilaterals, Circles, Cylinders, Cuboids & Spheres (Again.. too easy)

Heron's Formula

\- Area of a Triangle – by Heron’s Formula \- Application of Heron’s Formula

Trigonometry

\- Trigonometric Ratios, Identities \- Applications : Heights and Distances

Trigonometric Functions

\- Sum and Difference of Two Angles \- Trigonometric Equations \- Inverse Trigonometric Functions & their Properties

Circles

\- Tangent to a Circle

Straight Lines

\- Slope of a Line \- Forms of Equations of a Line \- Distance of a Point From a Line

Conic Sections

\- Cone, Circle, \- Equations: Parabola, Ellipse & Hyperbola \- Eccentricity, Latus rectum

Three Dimensional Geometry

\- Coordinate Axes and Coordinate Planes in 3D Space \- Coordinates of a Point in Space \- Distance between Two Points \- Section Formula \- Direction Cosines and Direction Ratios of a Line \- Equation of a Line in Space, Angle between Two Lines, Shortest Distance between Two Lines \- Plane \- Coplanarity of Two Lines \- Angle between Two Planes \- Distance of a Point from a Plane \- Angle between a Line and a Plane

------------------------------------------------------------------------------------------------------------------------------------------------

Some of the topics are obvious. Like the entire Calculus section from "Relations & Function" to "Integrals" & Vector Algebra.

And Stats and Probability.

But what about Binomial Theorem, Sequences & Series, Matrices & Determinants. And Complex Numbers.

Polynomials, Quadratics is fairly easy.

And what about he Geometry-ish section. Especially the entire Conic Sections and 3D Geometry. I am completely blanked on that. I can't remember it at all.

I can remember a fair amount of Trig and Straight Lines (Slope & distance etc). Not sure if that is needed. Trig Functions is probably important. (sine, cosine etc)

Thank very very much for even taking the time to read.

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go-travel-cpap-blog · 8 years ago

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NDA AND NAVAL DEFENCE ACADEMY

1. Algebra

The concept of a set, procedures on sets, Venn layouts. De Morgan laws. Cartesian product, relation, equivalence connection. Read More Representation of real figures on a line. Complicated numbers - basic qualities, modulus, argument, cube origins of unity. Binary program of numbers. Conversion associated with the number in decimal system to binary program and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. A solution of linear inequations of two variables simply by graphs. Permutation and Mixture. Binomial theorem and the application. Logarithms and their own applications. second. Matrices plus Determinants Forms of matrices, procedures on matrices Determinant associated with a matrix, basic qualities of the determinant. Adjoint plus inverse of a sq . matrix, Applications - Answer of a system associated with linear equations in 2 or three unknowns simply by Cramers rule and simply by Matrix Method. 3. Trigonometry Angles and their steps in degrees and within radians. Trigonometrical ratios. Trigonometric identities Sum and distinction formulae. Multiple and Sub-multiple angles. Inverse trigonometric features. Applications - Height plus distance, properties of triangles. 4. Analytical Geometry associated with two and three sizes Rectangular Cartesian Coordinate program. Distance formula. Equation associated with a line in the variety of forms. The position between two lines. The range of a point through a line. Equation associated with the circle in regular and general form. Regular types of the parabola, ellipse plus hyperbola. Eccentricity and axis of the conic. Stage in a 3d area, the distance between two factors. Direction Cosines and path ratios. The equation of the particular plane and a collection in a variety associated with forms. The angle between 2 lines and angle among two planes. Equation associated with the sphere. 5. Gear Calculus The concept of the real-valued function -- domain, range and chart of a function. Amalgamated functions, one to 1, onto and inverse features. Notion of limit, Regular limits - examples. Continuity of functions - good examples, algebraic operations on constant functions. Derivative of the function in a stage, geometrical and physical interpretation of a derivative -- applications. Derivatives of the amount, product and quotient associated with functions, a derivative of the function with respect associated with another function, derivative associated with a composite function. 2nd order derivatives. Increasing plus decreasing functions. The application associated with derivatives in problems associated with maxima and minima. six. Integral Calculus and Gear equations Integration as inverse of differentiation, integration simply by substitution and by components, standard integrals involving algebraic expressions, trigonometric, exponential plus hyperbolic functions. Evaluation associated with definite integrals - dedication of areas of aircraft regions bounded by the figure - applications. Definition associated with order and degree associated with a differential equation, development of a differential formula by examples. General plus the particular solution of the differential equation, solution associated with the first order and 1st-degree differential equations associated with various types - good examples. Application in problems associated with growth and decay. seven. Vector Algebra Vectors within two and three sizes, magnitude and direction associated with a vector. Unit plus null vectors, addition associated with vectors, scalar multiplication associated with the vector, scalar product or even dot product of two vectors. Vector product and mix product of two vectors. Applications-work did with the force and moment associated with the force and within geometrical problems. 8. Data and Possibility Statistics Category of data, Frequency submission, cumulative frequency distribution -- examples Graphical representation -- Histogram, Pie Chart, Rate of recurrence Polygon - examples. Steps of Central tendency -- mean, median and setting. Variance and standard change - determination and assessment. Correlation and regression. Possibility Random experiment, outcomes plus associated sample space, occasions, mutually exclusive and thorough events, impossible and particular events. Union and Intersection of events. Complementary, primary and composite events. Description of probability - traditional and statistical - good examples. Elementary theorems on the possibility - simple problems. Conditional probability, Bayes theorem -- simple problems. Random adjustable as a function on the particular sample space. Binomial submission, examples of random tests giving rise to Binominal distribution. Paper II COMMON ABILITY TEST Part The - ENGLISH

The query paper in English will certainly be designed to check the candidates understanding associated with English and workman such as utilisation of words. The syllabus covers various aspects such as Grammar and usage, language, comprehension and cohesion within extended text to check the candidate's proficiency within English.

Part B -- GENERAL UNDERSTANDING

The query paper on General Understanding will broadly cover the particular subjects Physics, Chemistry, Common Science, Social Studies, Location and Current Events. The particular syllabus given below will be designed to indicate the particular scope of these topics included in this papers. The topics mentioned are certainly not to be regarded because exhaustive and questions on topics of similar character not specifically mentioned in the syllabus can furthermore be asked. Candidates solutions are likely to show their own knowledge and intelligent knowing of the subject. Area A (Physics) Physical Qualities and States of Issue, Mass, Weight, Volume, Denseness and Specific Gravity, Theory of Archimedes, Pressure Measure. The motion of objects, Speed and Acceleration, Newton's Laws and regulations of Motion, Force plus Momentum, Parallelogram of Causes, Stability and Equilibrium associated with bodies, Gravitation, elementary suggestions of work, Power plus Energy. Effects of Warmth, Measurement of temperature plus heat, change of Condition and Latent Heat, Settings of transference of Warmth. Sound waves and their own properties, Simple musical devices. Rectilinear propagation of Gentle, Reflection and refraction. Circular mirrors and Lenses. Human being Eye. Natural and Synthetic Magnets, Properties of the Magnet, Earth like a Magnets. Static and Current Electrical power, conductors and nonconductors, Ohms Law, Simple Electrical Circuits, Heating, Lighting and Magnet effects of Current, Dimension of Electrical Power, Main and Secondary Cells, Make use of X-Rays.

#NDA #Vector Algebra

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jeniferdlanceau · 8 years ago

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South Korea's "first generation" of fully autonomous architects profiled in Rome exhibition

An office with a timber-lined courtyard, and another with bold red trusses are among the projects to feature in an exhibition of contemporary South Korean architecture in Rome.

The Sections of Autonomy Six Korean Architects exhibition at Fondazione Pastificio Cerere focuses on six architecture studios that were founded in South Korea between the 1990s and early 2000s, and now form the "backbone" of Korean architecture.

The chosen era is marked by political and cultural freedom in the country, following Japanese colonial rule in the early 20th century that suppressed and discontinued the country's culture and traditions.

In 1967, pioneering Korean architect Kim Swoo-gen sought to find a cultural identity free from Japanese influence and traditional Korean style. But it was not until 30 years later that this was mastered.

Exhibition curators Choi Won-joon and Luca Galofaro have chosen six architects who set up their studios during this time to highlight examples of this autonomous style.

"It was Kim Swoo-geeun's will to practice in autonomy, free from heavy ideological burdens, but it would take another thirty years for Korean architecture to finally arrive at that autonomous state," said exhibition co-curator Choi Won-joon. "Now in their early to late fifties age-wise, they build up the backbone of Korean architecture."

"As the first generation of Korean architects who were finally free from pressures to modernise tradition, or to form groups for active social engagement," added Choi, "they were able to fully explore the multiple dimensions of architectural autonomy and their reasoned individuality, through a practice rooted in local culture and conditions, yet thoroughly contemporaneous with international currents."

The selected architects are Choi Moon-gyu of GaA Architects, Jang Yoon-gyoo from Unsangdong Architects, Kim Jong-kyu of MARU, Kim Jun-sung of Architecture Studio Hand, Kim Seung-hoy of KYWC Architects and Kim Young-joon of YO2 Architects also feature in the showcase.

Sections of Autonomy Six Korean Architects will be on show at the Fondazione Pastificio Cerere in Rome from 7 to 21 February 2017.

Read on for curator Choi Woon-joon's descriptions of projects by the six architects:

H Music Library, Seoul, 2015, by Choi Moon-gyu

What alternatives can architecture provide in an urban context of endless facades? While its underground levels are fully occupied by a concert hall, on the ground level, where the music library is located, the building becomes an urban interstice', open to changing view, atmosphere, and program all year long.

Sited on the main street of Itawwon-ro that slopes from Namsan Mountain to the Hangang River, it was natural, both functionally and spatially, to form a ramp than to use stairs. With no visual or spatial obstacles, the curved surface of the ground floor exists as one continuum, providing pedestrians with various outdoor experiences and a fantastic Gangnam view that is otherwise blocked by rows of roadside buildings.

Soongsil University Student Union, Seoul, 2011, by Choi Moon-gyu

To minimise the impact on the adjacent square in the university's already dense campus, the new Student Union stretches out horizontally on the site. Utilising the site's 12 metre height difference to full advantage, almost half of the building is buried into the ground, suppressing the physical presence of a volume that contains 80 clubrooms, three cafeterias, a 200-seat theatre, administration offices, and stadium stands.

To allow natural ventilation and lighting, unique outdoor spaces are provided in three parts, one of which is the central stairway that functions as the building's spine, connecting the whole floors. With 25 entrances that lead visitors from every direction to a building with extensive relationship between outdoor and indoor spaces, the Student Union is a pathway itself, blurring the boundary between architecture and its surroundings.

Seongdong Cultural & Welfare Center, Seoul, 2010, by Jang Yoon-gyoo

Located in the centre of a low-income factory district in Seongsudong, Seongdong Cultural & Welfare Center, or Culture Forest, is more than a government office building, which is usually distanced from the citizens. As an active agent of urban regeneration, it physically inserts itself to the decaying urban environment to provide new programmes of cultural, industrial, and economic rehabilitation that will initiate change in the surrounding city and community.

By accommodating the city's horizontal streets, plazas, and elements of nature, this urban structure constructs an open three-dimensional public space, animated by diverse culture- and welfare-related programmes and interests.

Kring / KumHo Culture Complex, Seoul, 2006, by Jang Yoon-gyoo

As modern society demands companies to seek their own brand codes, architecture too becomes part of this strategy of identity and differentiation. This project attempts to transfer such requirement into an opportunity to experiment with ways of complementary and reciprocal communication between customers and companies.

In this project, a new set of programme diagrams capture new programmes and spatial possibilities for office environments, which the corporate client can promote as a feature of its own cultural identity. It aims to establish a "branded space", the proposed complex is a passage for communication with customers, a place for holding public performances, exhibitions, and competitions, aided by the intervention of art coordinators

Hansen Museum, Yeosu, 2015, by Kim Jong-kyu

Eayangwon is a destination for missionaries and leprosy sufferers, who found refuge there in 1927. It now includes modern and contemporary buildings, and an extension to a small museum was required to cope with a larger collection.

The design began with the question of relating the site's small hill with the church and the museum, hundred-year-old registered cultural properties. The site already had a strong sense of place, and this addition was to carefully follow the existing conditions and look as if it had been there all along. In the exhibition building, the placement of layers between vertical and horizontal spaces provides a rhythmical and dramatic experience to its visitors.

Arumjigi, Seoul, 2013, by Kim Jong-kyu

This head office for Arumjigi, a non-profit organisation for the protection and preservation of Korea's cultural heritage, is simple yet multifaceted: contrary to the generous and delicate appearance of the building facing the Hyoja-ro, the four story office finished with exposed concrete reticently faces the narrow and humble alley.

Since form is merely passive, relying on the volume and layout of its projected program, it is the material rather than the shape that is the distinguishing feature of Arumjigi at first glance. The essence of this building is the courtyard on the second floor, a space open to the sky and the wind, arranging a balanced harmony between the Hanok, a traditional house, and other buildings.

Humanist Books Office, Seoul, by Kim Jun-sung

The initiating goal of this office building for Humanist Publishing Co was not for functional efficiency but the creation of a place of communication with its neighbours. Only a few blocks away from the immensely popular Hongik University area, the site is located at the corner of a semi-residential area, and, with the size of 1,000-square-metres, is relatively tight.

However, even from the beginning, an outdoor open yard amidst an office environment was deemed essential for publishers whose work requires creativity and high concentration. This inner open yard runs through the whole body of office building, like a street stretching down to the underground auditorium and upwards to the top office floor, and its depth is reinforced by its glass facades with different inclinations.

KYWC Architects office, Soyul, Seoul, Kim Seung-hoy

KYWC Architects' own office building is situated at the foot of Namsan Mountain in the old alleys of Huam-dong. To fit the three above-ground floors within the height limit of 8.7 metres, the whole second floor was formed as a truss, minimising structure members of other floors. Coloured in red, the structural frames express the linear flow of force, while their flushed infill of spandrel glasses create a deceptively simple volume, within which all levels, from basement to roof garden, maintain their own spatial characteristics, corresponding to different programs, structures, and urban conditions.

The ground floor, for instance, a space for social gathering, is open to the city with minimum structure elements, reflecting the aims of this 'micro-cosmos' to integrate construction, program, and urban relationships into a singular system.

Hakhyunsa Publishing Co, Paju, 2008, by Kim Young-joon

This project, initiated at the end of the first stage of Paju Book City, was an extension of the long-term investigation on architecture with organisation of a city. From the premises concerning multiple approaches and flexible outcomes, to the relative positioning between the artificial and the natural, and the filled and the void, these factors were to be translated into architecture via a collective system, and such organisation was eventually made possible via a system of three compartmentalised groups in plans and sections.

The architectural solution to uncertain conditions was to create a connection of individual double-floor units. Avoiding a collective form of repeating unit-spaces, a collective system is attuned towards stacked-density, variety of spatial scales, and independence of interconnections.

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juliandmouton30 · 8 years ago

Text

South Korea's "first generation" of fully autonomous architects profiled in Rome exhibition

An office with a timber-lined courtyard, and another with bold red trusses are among the projects to feature in an exhibition of contemporary South Korean architecture in Rome.

Exhibition curators Choi Won-joon and Luca Galofaro have chosen six architects who set up their studios during this time to highlight examples of this autonomous style.

Sections of Autonomy Six Korean Architects will be on show at the Fondazione Pastificio Cerere in Rome from 7 to 21 February 2017.

Read on for curator Choi Woon-joon's descriptions of projects by the six architects:

H Music Library, Seoul, 2015, by Choi Moon-gyu

Soongsil University Student Union, Seoul, 2011, by Choi Moon-gyu

Seongdong Cultural & Welfare Center, Seoul, 2010, by Jang Yoon-gyoo

Kring / KumHo Culture Complex, Seoul, 2006, by Jang Yoon-gyoo

Hansen Museum, Yeosu, 2015, by Kim Jong-kyu

Arumjigi, Seoul, 2013, by Kim Jong-kyu

Humanist Books Office, Seoul, by Kim Jun-sung

KYWC Architects office, Soyul, Seoul, Kim Seung-hoy

Hakhyunsa Publishing Co, Paju, 2008, by Kim Young-joon

The post South Korea's "first generation" of fully autonomous architects profiled in Rome exhibition appeared first on Dezeen.

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