Multivariable Calculus and Mathematica®: With Applications to Geometry and Physics

Springer Science & Business Media, May 15, 1998 - Mathematics - 283 pages
0 Reviews
Reviews aren't verified, but Google checks for and removes fake content when it's identified
One of the authors' stated goals for this publication is to "modernize" the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present intoductions to geometry, mathematical physics, and kinematics, topics of particular interest to engineering and physical science students. In using Mathematica as a tool, the authors take pains not to use it simply to define things as a whole bunch of new "gadgets" streamlined to the taste of the authors, but rather they exploit the tremendous resources built into the program. They also make it clear that Mathematica is not algorithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The problem sets give students an opportunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numberical integration. They also cover the practice of incorporating text and headings into a Mathematica notebook. A DOS-formatted diskette accompanies the printed work, containing both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students. This supplementary work can be used with any standard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introductory primer for Mathematica.

What people are saying -Write a review

We haven't found any reviews in the usual places.

Contents

 INTRODUCTION 1 Benefits of Mathematical Software 2 Whats in This Book 3 Whats Not in This Book 4 How to Use This Book 5 A Word About Versions of Mathematica 7 REVIEW OF ONEVARIABLE CALCULUS 9 Glossary of Some Useful Mathematics Objects Commands 13
 DIRECTIONAL DERIVATIVES AND THE GRADIENT 95 Glossary of Some Useful Mathematics Objects Commands 101 GEOMETRY OF SURFACES 103 The Concept of a Surface 104 Basic Examples 105 The Implicit Function Theorem 110 Geometric Invariants 112 Curvature Calculations with Mathematica 119

 VECTORS AND GRAPHICS 17 Applications of Vectors 19 Parametric Curves 20 Graphing Surfaces 25 Parametric Surfaces 27 VECTORS AND GRAPHICS 29 Glossary of Some Useful Mathematics Objects Commands 33 GEOMETRY OF CURVES 35 Geometric Invariants 38 The Frenet Frame 39 Curvature and Torsion 41 Differential Geometry of Curves 43 The Osculating Circle 44 Spherical Curves 45 Helical Curves 46 Congruence 47 Two More Examples 48 The Astroid 49 The Cycloid 50 CURVES 53 Glossary of Some Useful Mathematica Objects Commands 62 KINEMATICS 65 Keplers Laws of Planetary Motion 68 Studying Equations of Motion with Mathematica 69 KINEMATICS 73 Glossary of Some Useful Mathematica Objects Commands 79 DIRECTIONAL DERIVATIVES 81 ThreeDimensional Graphs 82 Graphing Level Curves 83 The Gradient of a Function of Two Variables 86 Directional Derivatives 89 Functions of Three or More Variables 91
 SURFACES 123 Glossary of Some Useful Mathematica Objects Commands 129 OPTIMIZATION IN SEVERAL VARIABLES 133 Analytic Methods 134 Newtons Method 135 Functions of Two Variables 137 Second Derivative Test 138 Steepest Descent 139 Multivariable Newtons Method 141 Three or More Variables 142 OPTIMIZATION 145 Glossary of Some Useful Mathematica Objects 150 MULTIPLE INTEGRALS 153 Regions in the Plane 154 Viewing Simple Regions 156 Polar Regions 158 Viewing Solid Regions 161 A More Complicated Example 165 Cylindrical Coordinates 169 MULTIPLE INTEGRALS 173 Glossary of Some Useful Mathematica Objects Commands 182 PHYSICAL APPLICATIONS OF VECTOR CALCULUS 185 Newtonian Gravitation 188 Electricity and Magnetism 192 PHYSICAL APPLICATIONS 197 Glossary of Some Useful Mathematica Objects Commands 207 Energy Minimization and Laplaces Equation 208 MATHEMATICA TIPS 211 Glossary 225 Sample Notebook Solutions 239 Index 275 Copyright