Differential Equations

by Jeffrey R. Chasnov

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What follows are my lecture notes for a first course in differential equations.

Description from LibreTexts.

Publisher
Hong Kong University of Science and Technology
Subjects
Mathematics, Differential Equations
Licence
CC BY 3.0, 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: A Short Mathematical Review
  7. 1.1: The Trigonometric Functions
  8. 1.2: The Exponential Function and the Natural Logarithm
  9. 1.3: Definition of the Derivative
  10. 1.4: Differentiating a Combination of Functions
  11. 1.5: Differentiating Elementary Functions
  12. 1.6: Definition of the Integral
  13. 1.7: The Fundamental Theorem of Calculus
  14. 1.8: Definite and Indefinite Integrals
  15. 1.9: Indefinite Integrals of Elementary Functions
  16. 1.10: Substitution
  17. 1.11: Integration by Parts
  18. 1.12: Taylor Series
  19. 1.13: Functions of Several Variables
  20. 1.14: Complex Numbers
  21. 2: Introduction to ODEs
  22. 2.1: The Simplest Type of Differential Equation
  23. 3: First-Order ODEs
  24. 3.1: The Euler Method
  25. 3.2: Separable Equations
  26. 3.3: Linear Equations
  27. 3.4: Applications
  28. 4: Second-Order ODEs with Constant Coefficients
  29. 4.1: The Euler Method
  30. 4.2: The Principle of Superposition
  31. 4.3: The Wronskian
  32. 4.4: Homogeneous ODEs
  33. 4.5: Inhomogeneous ODEs
  34. 4.6: Inhomogeneous Linear First-Order ODEs Revisited
  35. 4.7: Resonance
  36. 4.8: Applications
  37. 4.9: Damped Resonance
  38. 5: The Laplace Transform
  39. 5.1: Definition and Properties
  40. 5.2: Solution of Initial Value Problems
  41. 5.3: Heaviside and Dirac Delta Functions
  42. 5.4: Discontinuous or Impulsive Terms
  43. 6: Series Solutions
  44. 6.1: Ordinary Points
  45. 6.2: Regular Singular Points - Cauchy-Euler Equations
  46. 7: Systems of Equations
  47. 7.1: Matrices, Determinants and the Eigenvalue Problem
  48. 7.2: Coupled First-Order Equations
  49. 7.3: Normal Modes
  50. 8: Nonlinear Differential Equations
  51. 8.1: Fixed Points and Stability
  52. 8.2: One-Dimensional Bifurcations
  53. 8.3: Two-Dimensional Bifurcations
  54. 9: Partial Differential Equations
  55. 9.1: Derivation of the Diffusion Equation
  56. 9.2: Derivation of the Wave Equation
  57. 9.3: Fourier Series
  58. 9.4: Fourier Sine and Cosine Series
  59. 9.5: Solution of the Diffusion Equation
  60. 9.6: Solution of the Wave Equation
  61. 9.7: The Laplace Equation
  62. 9.8: The Schrödinger Equation
  63. Back Matter
  64. Index
  65. Detailed Licensing