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Differential Equations with Mathematica
- 1st Edition - October 18, 1993
- Authors: Martha L Abell, James P. Braselton
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 1 3 9 1 - 0
Differential Equations with Mathematica presents an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as… Read more
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Request a sales quoteDifferential 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.
Preface
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
Index
- No. of pages: 640
- Language: English
- Edition: 1
- Published: October 18, 1993
- Imprint: Academic Press
- eBook ISBN: 9781483213910
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