最 低 价：￥146.00
定 价：￥162.27
作 者：Paul E. Waltman 著 著
出 版 社：Oversea Publishing House
出版时间：2004-4-1
I S B N：9780486434780
| Preface, ix 1 Systems of Linear Differential Equations 1. Introduction, 2. Some Elementary Matrix Algebra, 3. The Structure of Solutions of Homogeneous Linear Systems, 4. Matrix Analysis and the Matrix Exponential, 5. The Constant Coefficient Case: Real and Distinct Eigenvalues, 6. The Constant Coefficient Case: Complex and Distinct Eigenvalues, 7. The Constant Coefficient Case: The Putzer Algorithm, 8. General Linear Systems, 9. Some Elementary Stability Considerations, 10. Periodic Coefficients, 11. Scalar Equations, 12. An Application: Coupled Oscillators, 2 Two-Dimensional Autonomous Systems 1. Introduction, 2. The Phase Plane, 3. Critical Points of Some Special Linear Systems, 4. Critical Points of General Two-Dimensional LinearSystems, 5. Behavior of Nonlinear Two-Dimensional Systems Near a Critical Point, 6. Elementary Liapunov Stability Theory, 7. Limit Cycles and the Poincare-Bendixson Theorem, 8. An Example: Lotka-Volterra Competition, 9. An Example: The Simple Pendulum, 3 Existence Theory 1. Introduction, 2. Preliminaries, 3. The Contraction Mapping Theorem, 4. The Initial Value Problem for One Scalar Differential Equation, 5. The Initial Value Problem for Systems of Differential Equations, 6. An Existence Theorem for a Boundary Value Problem, 4 Boundary Value Problems 1. Introduction, 2. Linear Boundary Value Problems, 3. Oscillation and Comparison Theorems, 4. Sturm-Liouville Problems, 5. The Existence of Eigenvalues for Sturm-Liouville Problems 6. Two Properties of Eigenfunctions, 7. An Alternate Formulation-Integral Equations, 8. Eigenfunction Expansions, 9. The Inhomogeneous Sturm-Liouville Problem, 10. Some Standard Applications of Sturm-Liouville Theory, 11. Nonlinear Boundary Value Problems, |
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