Abell / Braselton Differential Equations with Mathematica

1. Auflage 2014
ISBN: 978-1-4832-1391-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 640 Seiten, Web PDF

Differential Equations with Mathematica presents an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Mathematica is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Mathematica can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are provided as well. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Autoren/Hrsg.

Abell, Martha L

Braselton, James P.

Inhaltsverzeichnis

1;Front Cover;1
2;Differential Equations with Mathematica;2
3;Copyright Page;3
4;Table of Contents;4
5;Preface;8
6;Chapter 1.
Introduction to Differential Equations;10
6.1;1.1 Purpose;10
6.2;1.2 Definitions and Concepts;10
6.3;1.3 Solutions of Differential Equations;13
6.4;1.4 Initial and Boundary Value Problems;14
7;Chapter 2.
First-Order Ordinary Differential Equations;17
7.1;2.1 Separation of Variables;17
7.2;2.2 Homogeneous Equations;23
7.3;2.3 Exact Equations;30
7.4;2.4 Linear Equations;35
7.5;2.5 Some Special First-Order Equations;44
7.6;2.6 Theory of First-Order Equations;59
8;Chapter 3.
Applications of First-Order Ordinary Differential Equations;63
8.1;3.1 Orthogonal Trajectories;63
8.2;3.2 Direction Fields;69
8.3;3.3 Population Growth and Decay;72
8.4;3.4 Newton's Law of Cooling;80
8.5;3.5 Free-Falling Bodies;84
9;Chapter 4.
Higher Order Differential Equations;99
9.1;4.1 Preliminary Definitions and Notation;99
9.2;4.2 Solutions of Homogeneous Equations with Constant Coefficients;106
9.3;4.3 Nonhomogeneous Equations with Constant Coefficients: The Annihilator Method;117
9.4;4.4 Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters;126
9.5;4.5 Ordinary Differential Equations with Nonconstant Coefficients: Cauchy-Euler Equations;144
9.6;4.6 Ordinary Differential Equations with Nonconstant Coefficients: Exact Second-Order, Autonomous, and Equidimensional Equations;151
10;Chapter 5.
Applications of Higher Order Differential Equations;169
10.1;5.1 Simple Harmonic Motion;169
10.2;5.2 Damped Motion;175
10.3;5.3 Forced Motion;188
10.4;5.4 L-R-C Circuits;205
10.5;5.5 Deflection of a Beam;208
10.6;5.6 The Simple Pendulum;212
11;Chapter 6.
Power Series Solutions of Ordinary Differential Equations;225
11.1;6.1 Power Series Review;225
11.2;6.2 Power Series Solutions about Ordinary Points;234
11.3;6.3 Power Series Solutions about Regular Singular Points;254
12;Chapter 7.
Applications of Power Series;281
12.1;7.1 Applications of Power Series Solutions to Cauchy-Euler Equations;281
12.2;7.2 The Hypergeometric Equation;289
12.3;7.3 The Vibrating Cable;299
13;Chapter 8.
Introduction to the Laplace Transform;303
13.1;8.1 The Laplace Transform: Preliminary Definitions and Notation;303
13.2;8.2 Solving Ordinary Differential Equations with the Laplace Transform;318
13.3;8.3 Some Special Equations: Delay Equations, Equations with
Nonconstant Coefficients;330
14;Chapter 9.
Applications of the Laplace Transform;348
14.1;9.1 Spring-Mass Systems Revisited;348
14.2;9.2 L-R-C Circuits Revisited;360
14.3;9.3 Population Problems Revisited;365
14.4;9.4 The Convolution Theorem;370
14.5;9.5 Differential Equations Involving Impulse Functions;379
15;Chapter 10.
Systems of Ordinary Differential Equations;387
15.1;10.1 Review of Matrix Algebra and Calculus;387
15.2;10.2 Preliminary Definitions and Notation;400
15.3;10.3 Homogeneous Linear Systems with Constant Coefficients;403
15.4;10.4 Variation of Parameters;428
15.5;10.5 Laplace Tra;439
15.6;10.6 Nonlinear Systems, Linearization, and Classification of Equilibrium Points;450
16;Chapter 11.
Applications of Systems of Ordinary Differential Equations;471
16.1;11.1 L-R-C Circuits with Loops;471
16.2;11.2 Diffusion Problems;486
16.3;11.3 Spring-Mass Systems;498
16.4;11.4 Population Problems;505
16.5;11.5 Applications Using Laplace Transforms;519
17;Chapter 12.
Fourier Series and Applications to Partial Differential Equations;537
17.1;12.1 Orthogonal Functions and Sturm-Liouville Problems;537
17.2;12.2 Introduction to Fourier Series;541
17.3;12.3 The One-Dimensional Heat Equation;561
17.4;12.4 The One-Dimensional Wave Equation;568
17.5;12.5 Laplace's Equation;572
17.6;12.6 The Two-Dimensional Wave Equation in a Circular Reg;579
18;Appendix: Numerical Methods;592
18.1;Euler's Method;592
18.2;The Runge-Kutta Method;599
18.3;Systems of Differential Equations;607
18.4;Error Analys;615
19;Glossary of Mathematica Commands;617
20;Selected References;634
21;Index;636