Differential equations with Mathematica / Martha L. Abell, James P. Braselton.

Format:

Book

Author/Creator:

Abell, Martha L., 1962-

Contributor:

Braselton, James P., 1965-

Language:

English

Subjects (All):

Differential equations--Data processing.

Differential equations.

Mathematica (Computer file).

Physical Description:

1 online resource (893 p.)

Edition:

3rd ed.

Place of Publication:

Amsterdam ; Boston : Elsevier Academic Press, c2004.

Language Note:

English

Summary:

The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

Contents:

Cover; Title Page; Copyright Page; Contents; Preface; Chapter 1. Introduction to Differential Equations; 1.1 Definitions and Concepts; 1.2 Solutions of Differential Equations; 1.3 Initial and Boundary-Value Problems; 1.4 Direction Fields; Chapter 2. First-Order Ordinary Differential Equations; 2.1 Theory of First-Order Equations: A Brief Discussion; 2.2 Separation of Variables; 2.3 Homogeneous Equations; 2.4 Exact Equations; 2.5 Linear Equations; 2.6 Numerical Approximations of Solutions to First-Order Equations; Chapter 3. Applications of First-Order Ordinary Differential Equations

3.1 Orthogonal Trajectories3.2 Population Growth and Decay; 3.3 Newton's Law of Cooling; 3.4 Free-Falling Bodies; Chapter 4. Higher-Order Differential Equations; 4.1 Preliminary Definitions and Notation; 4.2 Solving Homogeneous Equations with Constant Coefficients; 4.3 Introduction to Solving Nonhomogeneous Equations with Constant Coefficients; 4.4 Nonhomogeneous Equations with Constant Coefficients: The Method of Undetermined Coefficients; 4.5 Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters; 4.6 Cauchy-Euler Equations; 4.7 Series Solutions

4.8 Nonlinear EquationsChapter 5. Applications of Higher-Order Differential Equations; 5.1 Harmonic Motion; 5.2 The Pendulum Problem; 5.3 Other Applications; Chapter 6. Systems of Ordinary Differential Equations; 6.1 Review of Matrix Algebra and Calculus; 6.2 Systems of Equations: Preliminary Definitions and Theory; 6.3 Homogeneous Linear Systems with Constant Coefficients; 6.4 Nonhomogeneous First-Order Systems: Undetermined Coefficients, Variation of Parameters, and the Matrix Exponential; 6.5 Numerical Methods; 6.6 Nonlinear Systems, Linearization, and Classification of Equilibrium Points

Chapter 7. Applications of Systems of Ordinary Differential Equations7.1 Mechanical and Electrical Problems with First-Order Linear Systems; 7.2 Diffusion and Population Problems with First-Order Linear Systems; 7.3 Applications that Lead to Nonlinear Systems; Chapter 8. Laplace Transform Methods; 8.1 The Laplace Transform; 8.2 The Inverse Laplace Transform; 8.3 Solving Initial-Value Problems with the Laplace Transform; 8.4 Laplace Transforms of Step and Periodic Functions; 8.5 The Convolution Theorem; 8.6 Applications of Laplace Transforms, Part I; 8.7 Laplace Transform Methods for Systems

8.8 Applications of Laplace Transforms, Part IIChapter 9. Eigenvalue Problems and Fourier Series; 9.1 Boundary-Value Problems, Eigenvalue Problems, Sturm-Liouville Problems; 9.2 Fourier Sine Series and Cosine Series; 9.3 Fourier Series; 9.4 Generalized Fourier Series; Chapter 10. Partial Differential Equations; 10.1 Introduction to Partial Differential Equations and Separation of Variables; 10.2 The One-Dimensional Heat Equation; 10.3 The One-Dimensional Wave Equation; 10.4 Problems in Two Dimensions: Laplace's Equation; 10.5 Two-Dimensional Problems in a Circular Region

Appendix: Getting Started

Notes:

Includes bibliographical references ( p. 867-868) and index.

ISBN:

1-281-02076-1

9786611020767

0-08-052179-7

OCLC:

476073033