Ordinary Differential Equations

by Stephen Wiggins

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This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.

Description from LibreTexts.

Publisher
University of Bristol
Subjects
Mathematics, Differential Equations
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Getting Started - The Language of ODEs
  7. 1.1: Problem Set
  8. 2: Special Structure and Solutions of ODEs
  9. 2.1: Problem Set
  10. 3: Behavior Near Trajectories and Invariant Sets - Stability
  11. 3.1: Problem Set
  12. 4: Behavior Near Trajectories - Linearization
  13. 4.1: Problem Set
  14. 5: Behavior Near Equilbria - Linearization
  15. 5.1: Problem Set
  16. 6: Stable and Unstable Manifolds of Equilibria
  17. 6.1: Problem Set
  18. 7: Lyapunov’s Method and the LaSalle Invariance Principle
  19. 7.1: Lyapunov’s Method and the LaSalle Invariance Principle
  20. 7.2: Problem Set
  21. 8: Bifurcation of Equilibria I
  22. 8.1: Bifurcation of Equilibria I
  23. 8.2: Problem Set
  24. 9: Bifurcation of Equilibria II
  25. 9.1: Bifurcation of Equilibria II
  26. 9.2: Problem Set
  27. 10: Center Manifold Theory
  28. 10.1: Center Manifold Theory
  29. 10.E: Center Manifold Theory (Exericses)
  30. 11: Appendices
  31. 11.1: A- Jacobians, Inverses of Matrices, and Eigenvalues
  32. 11.2: B- Integration of Some Basic Linear ODEs
  33. 11.3: Finding Lyapunov Functions
  34. 11.4: D- Center Manifolds Depending on Parameters
  35. 11.5: E- Dynamics of Hamilton’s Equations
  36. Back Matter
  37. Index
  38. F: A Brief Introduction to the Characteristics of Chaos
  39. Index
  40. Detailed Licensing