Calculus and Vectors Nelson

ISBN:
0176374434 / 978176374433

Chapter 1 Introduction to Calculus

1.1 Radical Expressions Rationalizing Denominators

25

p.6

1.2 The Slope of a Tangent

56

p.10

1.3 Rates of Change

31

p.22

Mid Chapter Review Rates of Change

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1.4 Limit of a Function

34

p.34

1.5 Properties of Limits

43

p.40

1.6 Continuity

40

p.48

Chapter Review Limits and Continuity

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Chapter Test

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Chapter 2 Derivatives

2.1 The Derivative Function

48

p.65

2.2 The Derivatives of Polynomial Functions

70

p.76

2.3 The Product rule

35

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Mid Chapter Review upto Product Rule

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p.92

2.4 The Quotient Rule

37

p.94

2.5 Derivative of Composite Functions

54

p.99

Chapter Review Derivative Rules

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Chapter Test - Derivatives(Nel)

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Chapter 3 Derivatives and their Applications

3.1 High Order Derivatives, Velocities, and Acceleration

41

p.119

3.2 Max and Min on a Interval

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Mid Chapter Review Derivative Application

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3.3 Optimization Problems

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3.4 Optimization in Economics and Science

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Chapter Review Optimization

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Chapter Test on Optimization

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Chapter 4 Curve Sketching

4.1 Increasing and Decreasing Functions

36

p.165

4.2 Critical Points, Local Maxima, Local Minima

39

p.172

4.3 Vertical and Horizontal Asymptotes

47

p.181

Graphing Mid Chapter Review

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4.4 Concavity and Points of Inflection

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p.198

4.5 An Algorithm for Curve Sketching

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Chapter Review Curve Sketching

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Chapter Test Graphing

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Chapter 5 Derivatives of Exponential and Trigonometric Functions

5.1 Derivatives of Exponential Functions, y=e^x

45

p.227

5.2 Derivative of y =b^x

18

p.235

5.3 Optimization Problems Involving Exponential Functions

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p.241

Mid Chapter Review Derivatives of Exponential Functions

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5.4 The Derivatives of sinx and cosx

48

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5.5 Derivative of tan(x)

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5.6 Chapter Review Log and Trig Functions

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Chapter Test on Logs and Trig Derivatives

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Cumulative Calculus Review

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Chapter 6 Introduction to Vectors

6.0 Chapter Pre Req. Review of Trig

10

6.1 An Introduction to Vectors

25

p.275

6.2 Vector Addition

43

p.282

6.3 Multiplication of a Vector by a Scalar

45

p.293

6.4 Properties of Vectors

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p.302

Mid Chapter Review

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6.5 Vectors in 2D and 3D

48

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6.6 Operations with Algebraic Vectors in 2D

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6.7 Operation with Vectors in 3D

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6.8 Linear Combination and Spanning Sets

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p.334

Vectors Chapter Review

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Chapter 6 Test

11

Chapter 7 Applications of Vectors

7.1 Vectors as Forces

27

p.352

7.2 Vectors as Velocity

22

p.365

7.3 The Dot Product of Two Geometric Vectors

33

p.371

7.4 The Dot Product of Algebraic Vectors

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Mid Chapter Review

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7.5 Scalar and Vector Projections

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7.6 The Cross Product of Two Vectors

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7.7 Applications of Dot and Cross Product

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Applications of Vectors Chapter Review

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Chapter 8 Equations of Lines and Planes

8.1 Vector and Parametric Equations of a Line in 2D

23

p.427

8.2 Cartesian equation of a Line

30

p.435

8.3 Vector, Parametric and Symmetric Equations of a line in 3D

25

p.445

8.7 Mid Chapter Review

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8.4 Vector and Parametric Equations as Plane

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p.453

8.5 The Cartesian Equation of a Plane

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8.6 Sketching Planes in 3D

15

p.470

Chapter Review

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Chapter Test

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Chapter 9 Relations between Points, Lines and Planes

9.1 The intersection of a Line with a Plane and the Intersection of Two Lines

24

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9.2 System of Equations

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9.3 The Intersection of Two Planes

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9.4 The Intersection of Three Planes

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9.5 The Distance from a Point to a Line in R2

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9.6 The Distance from a Point to a Plane

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Relations between Points, Lines and Planes Chapter Review

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Relations between Points, Lines and Planes Test

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Vectors Cumulative Review

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