Calculus Projects Using Mathematica / Edition 1

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Overview

This book contains the Mathematica-based projects used in calculus at the Georgia Institute of Technology. Among the authors interests when writing these projects were to capture student interest through projects closely tied to their mathematics, science, and engineering curricula.
This book will enable students to demonstrate the applicability and effectiveness of mathematics in solving clearly relevant applied problems. Computing is used not as a gimmick, but as a genuine tool on problems where it really helps.
In this book, students will use calculus to understand the formation of rainbows, to study the flight of a baseball, to design some electrical circuits, to analyze an amusement park ride, to explain the reflections of a coffee cup, to design a rotary engine, and to solve many other interesting scientific problems.
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Product Details

  • ISBN-13: 9780070017900
  • Publisher: McGraw-Hill Higher Education
  • Publication date: 1/1/1996
  • Edition number: 1
  • Pages: 200
  • Product dimensions: 8.00 (w) x 10.00 (h) x 0.45 (d)

Table of Contents

A Mathematica Primer 1
Sample Project. The Green Monster in Fenway Park 10
Solution to Sample Project. The Green Monster 13
Project 1 Working with Functions and Graphs 22
Project 2 Reflections on Differentiation 28
Project 3 The Brightness of Venus 39
Project 4 Optimization 41
Project 5 The Arithmetic Mean - Geometric Mean Inequality 44
Project 6 Curves in Polar Coordinates 50
Project 7 Definite Integrals and Antiderivatives 58
Project 8 Computing Lengths of Elliptical Orbits 68
Project 9 Rainbows 73
Project 10 Several Applications of Integration 78
Project 11 Differential Equations: Euler's Method 80
Project 12 Differential Equations: Direction Fields 84
Project 13 Bungee Jumping 89
Project 14 Design of a DC Power Supply 93
Project 15 Taylor Polynomials 105
Project 16 Vector Functions and Parametric Curves 119
Project 17 Sliding Beads 124
Project 18 The Flying Teacups 127
Project 19 Envelopes of Families of Curves 129
Project 20 Surfaces and Extrema of Functions 136
Project 21 Constrained Optimization 144
Project 22 Multiple Integration 160
Project 23 Rolling Bodies 170
Project 24 Green's Theorem and Centroids 177
Project 25 The Wankel Rotary Engine 181
Project 26 Parametric Surfaces 193
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