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常微分方程与动力系统（影印版）

样章
作者：
Gerald Teschl
定价：
169.00 元
版面字数：
630千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2023年
ISBN：
978-7-04-055648-3
物料号：
55648-00
出版时间：
2021-03-22
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
常微分方程
暂无
  • 目录
    • 前辅文
      • Part 1. Classical theory
        • Chapter 1. Introduction
          • §1.1. Newton’s equations
            • §1.2. Classification of differential equations
              • §1.3. First-order autonomous equations
                • §1.4. Finding explicit solutions
                  • §1.5. Qualitative analysis of first-order equations
                    • §1.6. Qualitative analysis of first-order periodic equations
                    • Chapter 2. Initial value problems
                      • §2.1. Fixed point theorems
                        • §2.2. The basic existence and uniqueness result
                          • §2.3. Some extensions
                            • §2.4. Dependence on the initial condition
                              • §2.5. Regular perturbation theory
                                • §2.6. Extensibility of solutions
                                  • §2.7. Euler’s method and the Peano theorem
                                  • Chapter 3. Linear equations
                                    • §3.1. The matrix exponential
                                      • §3.2. Linear autonomous first-order systems
                                        • §3.3. Linear autonomous equations of order n
                                          • §3.4. General linear first-order systems
                                            • §3.5. Linear equations of order n
                                              • §3.6. Periodic linear systems
                                                • §3.7. Perturbed linear first-order systems
                                                  • §3.8. Appendix: Jordan canonical form
                                                  • Chapter 4. Differential equations in the complex domain
                                                    • §4.1. The basic existence and uniqueness result
                                                      • §4.2. The Frobenius method for second-order equations
                                                        • §4.3. Linear systems with singularities
                                                          • §4.4. The Frobenius method
                                                          • Chapter 5. Boundary value problems
                                                            • §5.1. Introduction
                                                              • §5.2. Compact symmetric operators
                                                                • §5.3. Sturm–Liouville equations
                                                                  • §5.4. Regular Sturm–Liouville problems
                                                                    • §5.5. Oscillation theory
                                                                      • §5.6. Periodic Sturm–Liouville equations
                                                                    • Part 2. Dynamical systems
                                                                      • Chapter 6. Dynamical systems
                                                                        • §6.1. Dynamical systems
                                                                          • §6.2. The flow of an autonomous equation
                                                                            • §6.3. Orbits and invariant sets
                                                                              • §6.4. The Poincar´e map
                                                                                • §6.5. Stability of fixed points
                                                                                  • §6.6. Stability via Liapunov’s method
                                                                                    • §6.7. Newton’s equation in one dimension
                                                                                    • Chapter 7. Planar dynamical systems
                                                                                      • §7.1. Examples from ecology
                                                                                        • §7.2. Examples from electrical engineering
                                                                                          • §7.3. The Poincar´e–Bendixson theorem
                                                                                          • Chapter 8. Higher dimensional dynamical systems
                                                                                            • §8.1. Attracting sets
                                                                                              • §8.2. The Lorenz equation
                                                                                                • §8.3. Hamiltonian mechanics
                                                                                                  • §8.4. Completely integrable Hamiltonian systems
                                                                                                    • §8.5. The Kepler problem
                                                                                                      • §8.6. The KAM theorem
                                                                                                      • Chapter 9. Local behavior near fixed points
                                                                                                        • §9.1. Stability of linear systems
                                                                                                          • §9.2. Stable and unstable manifolds
                                                                                                            • §9.3. The Hartman–Grobman theorem
                                                                                                              • §9.4. Appendix: Integral equations
                                                                                                            • Part 3. Chaos
                                                                                                              • Chapter 10. Discrete dynamical systems
                                                                                                                • §10.1. The logistic equation
                                                                                                                  • §10.2. Fixed and periodic points
                                                                                                                    • §10.3. Linear difference equations
                                                                                                                      • §10.4. Local behavior near fixed points
                                                                                                                      • Chapter 11. Discrete dynamical systems in one dimension
                                                                                                                        • §11.1. Period doubling
                                                                                                                          • §11.2. Sarkovskii’s theorem
                                                                                                                            • §11.3. On the definition of chaos
                                                                                                                              • §11.4. Cantor sets and the tent map
                                                                                                                                • §11.5. Symbolic dynamics
                                                                                                                                  • §11.6. Strange attractors/repellers and fractal sets
                                                                                                                                    • §11.7. Homoclinic orbits as source for chaos
                                                                                                                                    • Chapter 12. Periodic solutions
                                                                                                                                      • §12.1. Stability of periodic solutions
                                                                                                                                        • §12.2. The Poincar´e map
                                                                                                                                          • §12.3. Stable and unstable manifolds
                                                                                                                                            • §12.4. Melnikov’s method for autonomous perturbations
                                                                                                                                              • §12.5. Melnikov’s method for nonautonomous perturbations
                                                                                                                                              • Chapter 13. Chaos in higher dimensional systems
                                                                                                                                                • §13.1. The Smale horseshoe
                                                                                                                                                  • §13.2. The Smale–Birkhoff homoclinic theorem
                                                                                                                                                    • §13.3. Melnikov’s method for homoclinic orbits
                                                                                                                                                  • Bibliographical notes
                                                                                                                                                    • Bibliography
                                                                                                                                                      • Glossary of notation
                                                                                                                                                        • Index

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