Calclabs With Mathematica

by Hollis, Selwyn L.; Stewart, James

• ISBN13: 9780534364427
• ISBN10: 053436442X
• Edition: 4th
• Format: Paperback
• Copyright: 1999-05-28
• Publisher: Brooks Cole

Summary

A manual written to accompany the multivariable chapters of the fourth edition of James Stewart's Calculus, focusing on the use of Mathematica as a tool for exploring the way calculus works and how calculus solves problems. Coverage includes vectors, multiple integrals, and Mathematica basics. A final chapter contains 21 extended project exercises. Learning features include warning and tip icons, boxes on Mathematica commands, references to the main text, and within-chapter exercises.

Table of Contents

Introduction
Vectors	p. 1
Visualizing Vectors with Mathematica	p. 1
Length and Arithmetic Operations	p. 4
The Dot Product and Projections	p. 8
Exercises	p. 12
The Cross Product	p. 13
Equations of Lines	p. 18
Equations of Planes	p. 20
Exercises	p. 25
Surfaces	p. 27
Graphs of Functions of Two Variables	p. 27
Traces and Contours	p. 32
Exercises	p. 35
Cylindrical and Spherical Coordinates	p. 36
3D Contours and the Quadric Surfaces	p. 41
Exercises	p. 44
Vector-valued Functions	p. 45
Space Curves	p. 45
Exercises	p. 49
Derivatives	p. 50
Exercises	p. 52
Parametrization	p. 53
Arc Length and Curvature	p. 56
Velocity and Acceleration	p. 63
Exercises	p. 67
Parametric Surfaces: Vector-valued Functions of Two Variables	p. 68
Exercises	p. 72
Multivariate Functions	p. 73
Limits and Continuity	p. 73
Exercises	p. 78
Partial Derivatives	p. 78
Exercises	p. 83
The Tangent Plane and Linear Approximation	p. 83
Exercises	p. 87
Directional Derivatives and the Gradient	p. 87
Exercises	p. 99
Optimization and Lagrange Multipliers	p. 100
Exercises	p. 113
Multiple Integrals	p. 114
Double Integrals	p. 114
Polar Coordinates	p. 120
Applications	p. 122
Exercises	p. 125
Triple Integrals	p. 126
Cylindrical and Spherical Coordinates	p. 130
Exercises	p. 132
Change of Variables	p. 133
Exercises	p. 142
Vector Calculus	p. 144
Vector Fields	p. 144
Exercises	p. 150
Line Integrals	p. 151
Green's Theorem	p. 159
Exercises	p. 162
Surface Integrals	p. 162
Exercises	p. 168
Divergence, Curl, and the Laplacian	p. 169
Stokes' Theorem	p. 170
The Divergence Theorem	p. 172
Exercises	p. 174
Projects	p. 175
Osculating Circles	p. 175
Coriolis Acceleration	p. 176
An Ant on a Helix	p. 178
Animating Particle Motion	p. 178
Flying the Osculating Plane	p. 180
Drawing Curves on a Sphere	p. 181
Steepest Descent Curves	p. 184
Critical Point Classification	p. 186
Least Squares and Curve Fitting	p. 190
More Curve Fitting: Nonlinear Least Squares	p. 192
The Method of Steepest Descent	p. 194
Quadratic Approximation and Optimization	p. 198
Newton's Method for Nonlinear Equations	p. 201
Constrained Minimization with FindMinimum	p. 203
3D Coordinate Systems	p. 207
Rolling Marbles on Surfaces	p. 212
Balancing a Region	p. 215
Reflecting Points	p. 216
2D Space Exploration	p. 216
Streamlines I: Velocity Fields and Steady Flow	p. 219
Streamlines II: Incompressible Potential Flow	p. 221
Appendices	p. 224
Mathematica Basics	p. 224
Getting Started	p. 224
Functions	p. 234
Equations	p. 239
Lists	p. 241
Rules	p. 246
Graphics	p. 247
Packages	p. 253
Avoiding and Getting Out of Trouble	p. 254
Turning a Notebook into a Report	p. 257
Miscellaneous Issues	p. 259
The Arrow3D Package	p. 261
Recommended References and Resources	p. 263
Index	p. 264
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