Calculus and Vectors Nelson

ISBN:
0176374434 / 978176374433

Chapter 1 Introduction to Calculus

1.1 Radical Expressions Rationalizing Denominators

32

p.6

1.2 The Slope of a Tangent

52

p.10

1.3 Rates of Change

28

p.22

Mid Chapter Review Rates of Change

33

1.4 Limit of a Function

34

p.34

1.5 Properties of Limits

41

p.40

1.6 Continuity

30

p.48

Chapter Review Limits and Continuity

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55

Chapter Test

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14

Chapter 2 Derivatives

2.1 The Derivative Function

48

p.65

2.2 The Derivatives of Polynomial Functions

69

p.76

2.3 The Product rule

36

p.85

Mid Chapter Review upto Product Rule

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36

p.92

2.4 The Quotient Rule

39

p.94

2.5 Derivative of Composite Functions

55

p.99

Chapter Review Derivative Rules

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67

Chapter Test

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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

34

p.130

Mid Chapter Review Derivative Application

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23

3.3 Optimization Problems

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32

p.141

3.4 Optimization in Economics and Science

20

p.148

Chapter Review Optimization

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49

Chapter Test on Optimization

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13

Chapter 4 Curve Sketching

4.1 Increasing and Decreasing Functions

32

p.165

4.2 Critical Points, Local Maxima, Local Minima

46

p.172

4.3 Vertical and Horizontal Asymptotes

43

p.181

Graphing Mid Chapter Review

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40

4.4 Concavity and Points of Inflection

28

p.198

4.5 An Algorithm for Curve Sketching

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25

p.207

Chapter Review Curve Sketching

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39

Chapter Test Graphing

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7

Chapter 5 Derivatives of Exponential and Trigonometric Functions

5.1 Derivatives of Exponential Functions, y=e^x

47

p.227

5.2 Derivative of y =b^x

15

p.235

5.3 Optimization Problems Involving Exponential Functions

21

p.241

Mid Chapter Review Derivatives of Exponential Functions

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27

5.4 The Derivatives of sinx and cosx

48

p.250

5.5 Derivative of tan(x)

26

p.258

5.6 Chapter Review Log and Trig Functions

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56

Chapter Test on Logs and Trig Derivatives

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15

Cumulative Calculus Review

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76

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

40

p.282

6.3 Multiplication of a Vector by a Scalar

45

p.293

6.4 Properties of Vectors

20

p.302

6.5 Vectors in 2D and 3D

48

p.310

6.6 Operations with Algebraic Vectors in 2D

33

p.319

6.7 Operation with Vectors in 3D

34

p.327

6.8 Linear Combination and Spanning Sets

27

p.334

Introduction to Vectors Chapter Review

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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

28

p.371

7.4 The Dot Product of Algebraic Vectors

42

p.379

Mid Chapter Review

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7.5 Scalar and Vector Projections

29

p.390

7.6 The Cross Product of Two Vectors

31

p.401

7.7 Applications of Dot and Cross Product

22

p.409

Applications of Vectors Chapter Review

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70

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

24

p.445

8.7 Mid Chapter Review

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8.4 Vector and Parametric Equations as Plane

22

p.453

8.5 The Cartesian Equation of a Plane

23

p.461

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

p.489

9.2 System of Equations

22

p.499

9.3 The Intersection of Two Planes

25

p.510

9.4 The Intersection of Three Planes

43

p.520

9.5 The Distance from a Point to a Line in R2

30

p.534

9.6 The Distance from a Point to a Plane

21

p.542

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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