Differential Equations with Mathematica - 1st Edition - ISBN: 9780120415397, 9781483213910

Differential Equations with Mathematica

1st Edition

Authors: Martha L Abell James P. Braselton
eBook ISBN: 9781483213910
Imprint: Academic Press
Published Date: 18th October 1993
Page Count: 640
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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.

Table of Contents


Chapter 1: Introduction to Differential Equations

1.1 Purpose

1.2 Definitions and Concepts

1.3 Solutions of Differential Equations

1.4 Initial and Boundary Value Problems

Chapter 2: First-Order Ordinary Differential Equations

2.1 Separation of Variables

2.2 Homogeneous Equations

2.3 Exact Equations

2.4 Linear Equations

2.5 Some Special First-Order Equations

2.6 Theory of First-Order Equations

Chapter 3: Applications of First-Order Ordinary Differential Equations

3.1 Orthogonal Trajectories

3.2 Direction Fields

3.3 Population Growth and Decay

3.4 Newton's Law of Cooling

3.5 Free-Falling Bodies

Chapter 4: Higher Order Differential Equations

4.1 Preliminary Definitions and Notation

4.2 Solutions of Homogeneous Equations with Constant Coefficients

4.3 Nonhomogeneous Equations with Constant Coefficients: The Annihilator Method

4.4 Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters

4.5 Ordinary Differential Equations with Nonconstant Coefficients: Cauchy-Euler Equations

4.6 Ordinary Differential Equations with Nonconstant Coefficients: Exact Second-Order, Autonomous, and Equidimensional Equations

Chapter 5: Applications of Higher Order Differential Equations

5.1 Simple Harmonic Motion

5.2 Damped Motion

5.3 Forced Motion

5.4 L-R-C Circuits

5.5 Deflection of a Beam

5.6 The Simple Pendulum

Chapter 6: Power Series Solutions of Ordinary Differential Equations

6.1 Power Series Review

6.2 Power Series Solutions about Ordinary Points

6.3 Power Series Solutions about Regular Singular Points

Chapter 7: Applications of Power Series

7.1 Applications of Power Series Solutions to Cauchy-Euler Equations

7.2 The Hypergeometric Equation

7.3 The Vibrating Cable

Chapter 8: Introduction to the Laplace Transform

8.1 The Laplace Transform: Preliminary Definitions and Notation

8.2 Solving Ordinary Differential Equations with the Laplace Transform

8.3 Some Special Equations: Delay Equations, Equations with Nonconstant Coefficients

Chapter 9: Applications of the Laplace Transform

9.1 Spring-Mass Systems Revisited

9.2 L-R-C Circuits Revisited

9.3 Population Problems Revisited

9.4 The Convolution Theorem

9.5 Differential Equations Involving Impulse Functions

Chapter 10: Systems of Ordinary Differential Equations

10.1 Review of Matrix Algebra and Calculus

10.2 Preliminary Definitions and Notation

10.3 Homogeneous Linear Systems with Constant Coefficients

10.4 Variation of Parameters

10.5 Laplace Transforms

10.6 Nonlinear Systems, Linearization, and Classification of Equilibrium Points

Chapter 11: Applications of Systems of Ordinary Differential Equations

11.1 L-R-C Circuits with Loops

11.2 Diffusion Problems

11.3 Spring-Mass Systems

11.4 Population Problems

11.5 Applications Using Laplace Transforms

Chapter 12: Fourier Series and Applications to Partial Differential Equations

12.1 Orthogonal Functions and Sturm-Liouville Problems

12.2 Introduction to Fourier Series

12.3 The One-Dimensional Heat Equation

12.4 The One-Dimensional Wave Equation

12.5 Laplace's Equation

12.6 The Two-Dimensional Wave Equation in a Circular Region

Appendix: Numerical Methods

Euler's Method

The Runge-Kutta Method

Systems of Differential Equations

Error Analysis

Glossary of Mathematica Commands

Selected References



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© Academic Press 1993
Academic Press
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About the Author

Martha L Abell

James P. Braselton

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