Nguồn ngoài
A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems
These are notes for a second course in differential equations, covering linear and nonlinear systems and boundary value problems.
- Tác giả
- Russell Herman
- Nhà xuất bản
- University of North Carolina Wilmington
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 61 mục
- 01: Introduction and Review
- 1.01: 1.1 Review of the First Course
- 1.02: 1.2 Overview of the Course
- 1.03: 1.3 Appendix- Reduction of Order and Complex Roots
- 1.04: Problems
- 02: Systems of Differential Equations
- 2.01: Introduction
- 2.02: Equilibrium Solutions and Nearby Behaviors
- 2.03: Matrix Formulation
- 2.04: Eigenvalue Problems
- 2.05: Solving Constant Coefficient Systems in 2D
- 2.06: Examples of the Matrix Method
- 2.07: Theory of Homogeneous Constant Coefficient Systems
- 2.08: Nonhomogeneous Systems
- 2.09: Applications
- 2.10: Appendix- Diagonalization and Linear Systems
- 2.11: Problems
- 03: Nonlinear Systems
- 3.01: Introduction
- 3.02: Autonomous First Order Equations
- 3.03: Solution of the Logistic Equation
- 3.04: Bifurcations for First Order Equations
- 3.05: Nonlinear Pendulum
- 3.06: The Stability of Fixed Points in Nonlinear Systems
- 3.07: Nonlinear Population Models
- 3.08: Limit Cycles
- 3.09: Nonautonomous Nonlinear Systems
- 3.10: Appendix - Period of the Nonlinear Pendulum
- 3.11: Problems
- 04: Boundary Value Problems
- 4.01: Introduction
- 4.02: Partial Differential Equations
- 4.03: Connections to Linear Algebra
- 4.04: Problems
- 05: Fourier Series
- 5.01: Introduction to Fourier Series
- 5.02: Fourier Trigonometric Series
- 5.03: Fourier Series Over Other Intervals
- 5.04: Sine and Cosine Series
- 5.05: Appendix- The Gibbs Phenomenon
- 5.06: Problems
- 06: Sturm Liouville
- 6.01: Introduction
- 6.02: Properties of Sturm-Liouville Eigenvalue Problems
- 6.03: The Eigenfunction Expansion Method
- 6.04: The Fredholm Alternative Theorem
- 6.05: Problems
- 07: Special Functions
- 7.01: Classical Orthogonal Polynomials
- 7.02: Legendre Polynomials
- 7.03: Gamma Function
- 7.04: Bessel Functions
- 7.05: Hypergeometric Functions
- 7.06: Appendix- The Binomial Expansion
- 7.07: Problems
- 08: Green's Functions
- 8.01: The Method of Variation of Parameters
- 8.02: Initial and Boundary Value Green's Functions
- 8.03: Properties of Green's Functions
- 8.04: Series Representations of Green's Functions
- 8.05: Problems