Calculus and Vectors Nelson

ISBN:
0176374434 / 978176374433

Chapter 1 Introduction to Calculus

1.1 Radical Expressions Rationalizing Denominators

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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

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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

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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

39

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2.5 Derivative of Composite Functions

55

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

45

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

35

p.165

4.2 Critical Points, Local Maxima, Local Minima

47

p.172

4.3 Vertical and Horizontal Asymptotes

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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

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p.227

5.2 Derivative of y =b^x

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p.235

5.3 Optimization Problems Involving Exponential Functions

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Mid Chapter Review Derivatives of Exponential Functions

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5.4 The Derivatives of sinx and cosx

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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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Mid Chapter Review

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6.5 Vectors in 2D and 3D

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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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Introduction to Vectors Chapter Review

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Chapter 7 Applications of Vectors

7.1 Vectors as Forces

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p.352

7.2 Vectors as Velocity

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7.3 The Dot Product of Two Geometric Vectors

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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

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8.7 Mid Chapter Review

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8.4 Vector and Parametric Equations as Plane

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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

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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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