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Technology in Calculus: A Sourcebook of Activities / Edition 1

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More About This Textbook

Product Details

  • ISBN-13: 9780534930813
  • Publisher: Brooks/Cole
  • Publication date: 3/1/1992
  • Format: Mass Market Paperback
  • Edition number: 1
  • Pages: 200

Table of Contents

Introduction: Using Technology to Study Calculus 1
1 Graphing as a Tool 11
1.1 Solving Equations Graphically 12
1.2 Solving Inequalities Graphically 17
1.3 Investigating Function Parameters Graphically 21
2 Exploring Functions Behavior 25
2.1 Exploring Limits Numerically 26
2.2 Exploring Limits Graphically 31
2.3 Exploring Continuity Graphically 36
2.4 Horizontal Asymptotes and End Behavior 44
3 Understanding the Derivative 49
3.1 Estimating Derivatives Numerically 51
3.2 Estimating Derivatives Graphically 56
3.3 Plotting the Difference Quotient Function 62
3.4 Best Linear Approximations 63
4 Curves and Derivatives 65
4.1 Critical Points and the First Derivative Test 66
4.2 Inflection Points and the Second Derivative Test 67
4.3 The Mean Value Theorem 69
4.4 Curvature and the Osculating Circle 70
4.5 Best Quadratic Approximations 73
5 Understanding Integration 75
5.1 Discovering the Fundamental Theorems of Calculus 76
5.2 Numerical Techniques of Integration 80
5.3 Error Estimates for Trapezoidal and Simpson's Rules 92
6 Slopefields, Antiderivatives, and Differential Equations 99
6.1 Recovering a Function's Graph from Its Slope 100
6.2 Slopefields and Differential Equations 105
6.3 Euler's Method 109
7 Parametric and Polar Equations 113
7.1 Parametric Plotting 114
7.2 Polar Coordinates 117
7.3 Polar Plotting 122
7.4 Area and Polar Coordinates 128
8 Finding Roots and Fixed Points 130
8.1 The Bisection Method 132
8.2 Newton's Method 136
8.3 Fixed Points - Criteria for Convergence of Newton's Method 141
9 Function Approximations 154
9.1 Zooming as an Analytic Tool 155
9.2 Comparing Taylor Polynomials 161
9.3 Cubic Splines 163
Appendix: Answers to Activity Exercises 177
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