Table of contents for Differential equations with Mathematica / Martha L. Abell, James P. Braselton.
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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. Homogeneous Equations. Exact Equations. Linear Equations. Numerical Approximations of Solutions to First-Order Equations.Applications of First-Order Ordinary Differential Equations: Orthogonal Trajectories. Population Growth and Decay. Newton's Law of Cooling. Free-Falling Bodies. Higher-Order Differential Equations: Preliminary Definitions and Notation. Solving Homogeneus Equations with Constant Coefficients. Introduction to Solving Nonhomogeneus Equations with Constant Coefficients. Nonhomogeneous Equations with Constant Coefficients. The Method of Undetermined Coefficients. Nonhomogeneus Equations with Constant Coefficients. Variation of Parameters Applications of Higher-Order Differential Equations: Simple Harmonic Motion. Damped Motion. Forced Motion. Other Applications. The Pendulum Problem Ordinary Differential Equations with Nonconstant Coefficients: Cauchy-Euler Equations. Power Series Review. Power Series Solutions About Ordinary Points. Series Solutions about Regular Singular Points. Some Special Functions Laplace Transform Methods: The Laplace Transform. The Inverse Laplace Transform. Solving Initial-Value Problems with the Laplace Transform. Laplace Transforms of Step and Periodic Functions. The Convolution Theorem. Applications of Laplace Transforms. Systems of Ordinary Differential Equations: Review of Matrix Algebra and Calculus. Systems of Equations: Preliminary Definitions and Theory. Homogeneous Linear Systems with Constant Coefficients. Nonhomeogeneous First-Order Systems: Undetermined Coefficients, Variation of Parameters and the Matrix Exponential. The Laplace Transform Methods Numerical Methods, Nonlinear Systems, Linearization, and Classificaction 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 using Laplace Transforms. Applications that Lead to Nonlinear Systems Biological Systems Eigenvalue Problems and Fourier Series: Boundary Value 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. Appendix: Getting Started.
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