Computer Algebra Recipes

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5.2. DIFFUSION AND LAPLACE'S EQUATION MODELS 245 With this simple example under his belt, Hugo feels con¯dent that if he can come up with some °uid °ow examples for di®erent hull shapes, he might make a good impression on his interviewers and be hired. He realizes that for more complicated shapes he will probably have to use Maple's numerical capability. So let's leave Hugo to ¯nish his job interview preparation, so he doesn't pull aRockHudsonandgiveabadinterview. PROBLEMS: Problem 5-28: Split potential On the surface of a hollow sphere of radius a, the electric potential is ½ +V; 0 · μ
Chapter 6 Linear PDE Models. Part 2 In the previous chapter, the computer algebra recipes concentrated on mathematical models formulated in terms of the di®usion and Laplace equations. In this continuation of our study of linear PDE models, the wave equation and a variety of models involving semi-in¯nite and in¯nite domains are presented. 6.1 Wave Equation Models Thewaveequation, r 2 Ã(~r; t) = 1 c2 @2Ã(~r; t) @t2 ; (6.1) with r2 the Laplace operator, Ã a scalar or vector function of position ~r and time t, andcthe wave velocity, applies to many di®erent types of waves, e.g., ² electromagnetic waves (with Ã a vector); ² sound waves; ² tidal waves in an incompressible °uid; ² elastic waves in a solid; ² vibrations of elastic strings and membranes. In our ¯rst example, Vectoria plucks the humble string. 6.1.1 Vectoria Encounters Simon Legree \We called him Tortoise because he taught us," said the Mock Turtle angrily. \Really you are very dull!" Lewis Carroll, Alice's Adventures in Wonderland, 1865 It is some time later in the undergraduate career of Vectoria, the physics student who has been featured in several of our earlier stories. Recall that, inspired by the movie Casablanca, Vectoria used Maple to check and animate a textbook formula for the transverse motion of an initially horizontal piano string that has been struck. Since then Vectoria has progressed in her studies and is currently enrolled in a mathematical physics course. She has begun to learn how to solve wave equation problems using the separation of variables method. 247
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Richard H. Enns George C. McGuire C
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PREFACE A computer algebra system (
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viii CONTENTS 2.3.1 Finite Di®eren
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x CONTENTS 8.3 The Bifurcation Diag
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2 INTRODUCTION B. Computer Algebra
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4 INTRODUCTION (a) At what angle Á
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6 INTRODUCTION The negative answer
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8 INTRODUCTION D. Maple Help We tea
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Part I THE APPETIZERS A man ceases
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14 CHAPTER 1. PHASE-PLANE PORTRAITS
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48 CHAPTER 2. PHASE-PLANE ANALYSIS
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Chapter 3 Linear ODE Models Among a
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3.1. FIRST-ORDER MODELS 111 Therate
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3.1. FIRST-ORDER MODELS 113 Pressur
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3.1. FIRST-ORDER MODELS 115 3.1.2 G
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3.1. FIRST-ORDER MODELS 117 Evil Kn
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3.2. SECOND-ORDER MODELS 119 > tf:=
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3.2. SECOND-ORDER MODELS 121 3.2.2
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3.2. SECOND-ORDER MODELS 123 Loadin
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3.2. SECOND-ORDER MODELS 125 0.4 0.
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3.2. SECOND-ORDER MODELS 127 On ent
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3.2. SECOND-ORDER MODELS 129 Using
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3.3. SPECIAL FUNCTION MODELS 131 3.
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3.3. SPECIAL FUNCTION MODELS 133 1
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3.3. SPECIAL FUNCTION MODELS 135 Th
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3.3. SPECIAL FUNCTION MODELS 137 3.
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3.3. SPECIAL FUNCTION MODELS 139 th
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3.3. SPECIAL FUNCTION MODELS 141 PR
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3.3. SPECIAL FUNCTION MODELS 143 ¡
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3.3. SPECIAL FUNCTION MODELS 145 μ
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3.3. SPECIAL FUNCTION MODELS 147 >
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150 CHAPTER 4. NONLINEAR ODE MODELS
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298 CHAPTER 7. THE HUNT FOR SOLITON
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320 CHAPTER 8. NONLINEAR DIAGNOSTIC
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356 BIBLIOGRAPHY [Dav62] H. T. Davi
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358 BIBLIOGRAPHY [Nyq28] H. Nyquist
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Index acoustical waveguide, 261 ade
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INDEX 363 eigenvalue, 130 Eiram Eir
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INDEX 365 Help, Full Text Search, 8
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INDEX 367 laplace, 121,267,268 lhs,
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INDEX 369 ¯sh harvesting, 100 ¯xe
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INDEX 371 quartic map, 345 Queen Di
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Computer Algebra Recipes

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