Phu Xuan University Library
|
PXU E-LIB
Sign in
A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems

External

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.

Differential EquationsMathematics
Author
Russell Herman
Publisher
University of North Carolina Wilmington
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 61 sections
  1. 01: Introduction and Review
  2. 1.01: 1.1 Review of the First Course
  3. 1.02: 1.2 Overview of the Course
  4. 1.03: 1.3 Appendix- Reduction of Order and Complex Roots
  5. 1.04: Problems
  6. 02: Systems of Differential Equations
  7. 2.01: Introduction
  8. 2.02: Equilibrium Solutions and Nearby Behaviors
  9. 2.03: Matrix Formulation
  10. 2.04: Eigenvalue Problems
  11. 2.05: Solving Constant Coefficient Systems in 2D
  12. 2.06: Examples of the Matrix Method
  13. 2.07: Theory of Homogeneous Constant Coefficient Systems
  14. 2.08: Nonhomogeneous Systems
  15. 2.09: Applications
  16. 2.10: Appendix- Diagonalization and Linear Systems
  17. 2.11: Problems
  18. 03: Nonlinear Systems
  19. 3.01: Introduction
  20. 3.02: Autonomous First Order Equations
  21. 3.03: Solution of the Logistic Equation
  22. 3.04: Bifurcations for First Order Equations
  23. 3.05: Nonlinear Pendulum
  24. 3.06: The Stability of Fixed Points in Nonlinear Systems
  25. 3.07: Nonlinear Population Models
  26. 3.08: Limit Cycles
  27. 3.09: Nonautonomous Nonlinear Systems
  28. 3.10: Appendix - Period of the Nonlinear Pendulum
  29. 3.11: Problems
  30. 04: Boundary Value Problems
  31. 4.01: Introduction
  32. 4.02: Partial Differential Equations
  33. 4.03: Connections to Linear Algebra
  34. 4.04: Problems
  35. 05: Fourier Series
  36. 5.01: Introduction to Fourier Series
  37. 5.02: Fourier Trigonometric Series
  38. 5.03: Fourier Series Over Other Intervals
  39. 5.04: Sine and Cosine Series
  40. 5.05: Appendix- The Gibbs Phenomenon
  41. 5.06: Problems
  42. 06: Sturm Liouville
  43. 6.01: Introduction
  44. 6.02: Properties of Sturm-Liouville Eigenvalue Problems
  45. 6.03: The Eigenfunction Expansion Method
  46. 6.04: The Fredholm Alternative Theorem
  47. 6.05: Problems
  48. 07: Special Functions
  49. 7.01: Classical Orthogonal Polynomials
  50. 7.02: Legendre Polynomials
  51. 7.03: Gamma Function
  52. 7.04: Bessel Functions
  53. 7.05: Hypergeometric Functions
  54. 7.06: Appendix- The Binomial Expansion
  55. 7.07: Problems
  56. 08: Green's Functions
  57. 8.01: The Method of Variation of Parameters
  58. 8.02: Initial and Boundary Value Green's Functions
  59. 8.03: Properties of Green's Functions
  60. 8.04: Series Representations of Green's Functions
  61. 8.05: Problems