Differential Equations and Boundary Value Problems: Computing and Modeling, CourseSmart eTextbook, 4th Edition

For introductory courses in Differential Equations.

This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.

Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.

Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method, and Improvements. The Runge-Kutta Method.

Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.

First-Order Systems and Applications. The Method of Elimination. Numerical Methods for Systems.

Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogenous Linear Systems.

Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. Chaos in Dynamical Systems.

Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.

Introduction and Review of Power Series. Series Solutions Near Ordinary Points. Regular Singular Points. Method of Frobenius: The Exceptional Cases. Bessel's Equation. Applications of Bessel Functions.

Periodic Functions and Trigonometric Series. General Fourier Series and Convergence. Even-Odd Functions and Termwise Differentiation. Applications of Fourier Series. Heat Conduction and Separation of Variables. Vibrating Strings and the One-Dimensional Wave Equation. Steady-State Temperature and Laplace's Equation.

Sturm-Liouville Problems and Eigenfunction Expansions. Applications of Eigenfunction Series. Steady Periodic Solutions and Natural Frequencies. Applications of Bessel Functions. Higher-Dimensional Phenomena.