Abell M.L., Braselton J.P. Differential equations with Mathematica

Third Edition. — Academic Press, 2004. — 876 p.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.Introduction to Differential Equations.
Definitions and Concepts.
Solutions of Differential Equations.
Initial and Boundary-Value Problems.
Direction Fields.First-Order Ordinary Differential Equations.
Theory of First-Order Equations: A Brief Discussion.
Separation of Variables. Application: Kidney Dialysis.
Homogeneous Equations. Application: Models of Pursuit.
Exact Equations.
Linear Equations.
Numerical Approximations of Solutions to First-Order Equations.Applications of First-Order Ordinary Differential Equations.
Orthogonal Trajectories. Application: Oblique Trajectories.
Population Growth and Decay.
Newton’s Law of Cooling.
Free-Falling Bodies.Higher-Order Differential Equations.
Preliminary Definitions and Notation.
Solving Homogeneous Equations with Constant Coefficients.
Introduction to Solving Nonhomogeneous Equations with Constant Coefficients.
Nonhomogeneous Equations with Constant Coefficients: The Method of Undetermined Coefficients.
Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters.
Cauchy–Euler Equations.
Series Solutions.
Nonlinear Equations.Applications of Higher-Order Differential Equations.
Harmonic Motion.
The Pendulum Problem.
Other Applications.Systems of Ordinary Differential Equations.
Review of Matrix Algebra and Calculus.
Systems of Equations: Preliminary Definitions and Theory.
Homogeneous Linear Systems with Constant Coefficients.
Nonhomogeneous First-Order Systems: Undetermined Coefficients, Variation of Parameters, and the Matrix Exponential.
Numerical Methods.
Nonlinear Systems, Linearization, and Classification of Equilibrium Points.Applications of Systems of Ordinary Differential Equations.
Mechanical and Electrical Problems with First-Order Linear Systems.
Diffusion and Population Problems with First-Order Linear Systems.
Applications that Lead to Nonlinear Systems.Laplace Transform Methods.
The Laplace Transform.
The Inverse Laplace Transform.
Laplace Transforms of Step and Periodic Functions.
The Convolution Theorem.
Applications of Laplace Transforms, Part I.
Laplace Transform Methods for Systems.
Applications of Laplace Transforms, Part II.8Eigenvalue Problems and Fourier Series.
Boundary-Value Problems, Eigenvalue Problems, Sturm–Liouville Problems.
Fourier Sine Series and Cosine Series.
Fourier Series.
Generalized Fourier Series.Partial Differential Equations.
Introduction to Partial Differential Equations and Separation of Variables.
The One-Dimensional Heat Equation.
The One-Dimensional Wave Equation.
Problems in Two Dimensions: Laplace’s Equation.
Two-Dimensional Problems in a Circular Region.