Elsevier S & T

Differential Equations with Mathematica

Abell, Martha L.; Braselton, James P.

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Table of contents
  • Cover
  • Title Pageiii
  • Copyright Pageiv
  • Contentsv
  • Prefacexiii
  • Chapter 1. Introduction to Differential Equations1
  • 1.1 Definitions and Concepts2
  • 1.2 Solutions of Differential Equations6
  • 1.3 Initial and Boundary-Value Problems18
  • 1.4 Direction Fields26
  • Chapter 2. First-Order Ordinary Differential Equations41
  • 2.1 Theory of First-Order Equations: A Brief Discussion41
  • 2.2 Separation of Variables46
  • 2.3 Homogeneous Equations59
  • 2.4 Exact Equations69
  • 2.5 Linear Equations74
  • 2.6 Numerical Approximations of Solutions to First-Order Equations92
  • Chapter 3. Applications of First-Order Ordinary Differential Equations119
  • 3.1 Orthogonal Trajectories119
  • 3.2 Population Growth and Decay132
  • 3.3 Newton’s Law of Cooling157
  • 3.4 Free-Falling Bodies163
  • Chapter 4. Higher-Order Differential Equations175
  • 4.1 Preliminary Definitions and Notation175
  • 4.2 Solving Homogeneous Equations with Constant Coefficients196
  • 4.3 Introduction to Solving Nonhomogeneous Equations with Constant Coefficients216
  • 4.4 Nonhomogeneous Equations with Constant Coefficients: The Method of Undetermined Coefficients222
  • 4.5 Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters248
  • 4.6 Cauchy–Euler Equations255
  • 4.7 Series Solutions268
  • 4.8 Nonlinear Equations304
  • Chapter 5. Applications of Higher-Order Differential Equations321
  • 5.1 Harmonic Motion321
  • 5.2 The Pendulum Problem373
  • 5.3 Other Applications387
  • Chapter 6. Systems of Ordinary Differential Equations411
  • 6.1 Review of Matrix Algebra and Calculus411
  • 6.2 Systems of Equations: Preliminary Definitions and Theory427
  • 6.3 Homogeneous Linear Systems with Constant Coefficients454
  • 6.4 Nonhomogeneous First-Order Systems: Undetermined Coefficients, Variation of Parameters, and the485
  • 6.5 Numerical Methods506
  • 6.6 Nonlinear Systems, Linearization, and Classification of Equilibrium Points535
  • Chapter 7. Applications of Systems of Ordinary Differential Equations567
  • 7.1 Mechanical and Electrical Problems with First-Order Linear Systems567
  • 7.2 Diffusion and Population Problems with First-Order Linear Systems576
  • 7.3 Applications that Lead to Nonlinear Systems587
  • Chapter 8. Laplace Transform Methods617
  • 8.1 The Laplace Transform618
  • 8.2 The Inverse Laplace Transform629
  • 8.3 Solving Initial-Value Problems with the Laplace Transform637
  • 8.4 Laplace Transforms of Step and Periodic Functions645
  • 8.5 The Convolution Theorem667
  • 8.6 Applications of Laplace Transforms, Part I672
  • 8.7 Laplace Transform Methods for Systems691
  • 8.8 Applications of Laplace Transforms, Part II708
  • Chapter 9. Eigenvalue Problems and Fourier Series727
  • 9.1 Boundary-Value Problems, Eigenvalue Problems, Sturm–Liouville Problems727
  • 9.2 Fourier Sine Series and Cosine Series737
  • 9.3 Fourier Series749
  • 9.4 Generalized Fourier Series770
  • Chapter 10. Partial Differential Equations783
  • 10.1 Introduction to Partial Differential Equations and Separation of Variables783
  • 10.2 The One-Dimensional Heat Equation787
  • 10.3 The One-Dimensional Wave Equation799
  • 10.4 Problems in Two Dimensions: Laplace’s Equation810
  • 10.5 Two-Dimensional Problems in a Circular Region817
  • Appendix: Getting Started841
  • Introduction to Mathematica841
  • Loading Packages850
  • Getting Help from Mathematica854
  • The Mathematica Menu863
  • Bibliography865
  • Index867
Book details
  • Vendor Elsevier S & T
  • SKU 9780120415625
  • ISBN-13 9780080521794
  • Author Abell, Martha L.; Braselton, James P.
  • Edition 3rd
  • Category Mathematics
  • Subject Applied

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Description eBook delivery & access Reviews
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