Differential Equations and Linear Algebra / Edition 1by C. Henry Edwards, David E. Penney
Pub. Date: 07/11/2000
Publisher: Pearson Education
This tried-and-true book of differential equations expands upon the authors' Differential Equations: Computing and Modeling, 2nd Edition. It covers the core concepts and techniques of elementary linear algebramatrices and linear systems, vector spaces, eigensystems, and matrix exponentialsthat are needed for a careful introduction to linear equations. Complimenting this solid foundation, the book emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout. Chapter topics include: first order differential equations, mathematical models and numerical methods, linear systems and matrices, vector spaces, linear equations of higher order, eigenvalues and eigenvectors, linear systems of differential equations, matrix exponential methods, and nonlinear systems and phenomena. A geometric visualization for those interested in science and engineering.
- Pearson Education
- Publication date:
- Edition description:
- Older Edition
- Product dimensions:
- 8.20(w) x 9.30(h) x 1.30(d)
Table of Contents1. First-Order Differential Equations.
Differential Equations and Mathematical Model. Integrals as General and Particular Solutions. Direction Fields and Solution Curves. Separable Equations and Applications. Linear First-Order Equations. Substitution Methods and Exact Equations.
2. Mathematical Models and Numerical Methods.
Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method. The Runge-Kutta Method.
3. Linear Systems and Matrices.
Introduction to Linear Systems. Matrices and Gaussian Elimination. Reduced Row-Echelon Matrices. Matrix Operations. Inverses of Matrices. Determinants. Linear Equations and Curve Fitting.
4. Vector Spaces.
The Vector Space R^3. The Vector Space R
5. Linear Equations of Higher Order.
Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Undetermined Coefficients and Variation of Parameters. Forced Oscillations and Resonance.
6. Eigenvalues and Eigenvectors.
Introduction to Eigenvalues. Diagonalization of Matrices. Applications Involving Powers of Matrices.
7. Linear Systems of Differential Equations.
First-Order Systems and Applications. Matrices and Linear Systems. The Eigenvalue Method for Linear Systems. Second-Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Numerical Methods for Systems.
8. Matrix Exponential Methods.
Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems. Spectral Decomposition Methods.
9. Nonlinear Systems and Phenomena.
Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems.
10. Laplace Transform Methods.
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.
11. Power Series Methods.
Introduction and Review of Power Series. Power Series Solutions. Frobenius Series Solutions. Bessel's Equation.
References for Further Study.
Appendix A: The Existence and Uniqueness of Solutions.
Appendix B: Theory of Determinants.
Answers to Selected Problems.
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