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Differential Equations

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Differential Equations

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

Differential EquationsMathematics
Tác giả
Jeffrey R. Chasnov
Nhà xuất bản
Hong Kong University of Science and Technology
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LibreTexts
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CC BY
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EN
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Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 57 mục
  1. 01: A Short Mathematical Review
  2. 1.01: The Trigonometric Functions
  3. 1.02: The Exponential Function and the Natural Logarithm
  4. 1.03: Definition of the Derivative
  5. 1.04: Differentiating a Combination of Functions
  6. 1.05: Differentiating Elementary Functions
  7. 1.06: Definition of the Integral
  8. 1.07: The Fundamental Theorem of Calculus
  9. 1.08: Definite and Indefinite Integrals
  10. 1.09: Indefinite Integrals of Elementary Functions
  11. 1.10: Substitution
  12. 1.11: Integration by Parts
  13. 1.12: Taylor Series
  14. 1.13: Functions of Several Variables
  15. 1.14: Complex Numbers
  16. 02: Introduction to ODEs
  17. 2.01: The Simplest Type of Differential Equation
  18. 03: First-Order ODEs
  19. 3.01: The Euler Method
  20. 3.02: Separable Equations
  21. 3.03: Linear Equations
  22. 3.04: Applications
  23. 04: Second-Order ODEs Constant Coefficients
  24. 4.01: The Euler Method
  25. 4.02: The Principle of Superposition
  26. 4.03: The Wronskian
  27. 4.04: Homogeneous ODEs
  28. 4.05: Inhomogeneous ODEs
  29. 4.06: Inhomogeneous Linear First-Order ODEs Revisited
  30. 4.07: Resonance
  31. 4.08: Applications
  32. 4.09: Damped Resonance
  33. 05: The Laplace Transform
  34. 5.01: Definition and Properties
  35. 5.02: Solution of Initial Value Problems
  36. 5.03: Heaviside and Dirac Delta Functions
  37. 5.04: Discontinuous or Impulsive Terms
  38. 06: Series Solutions
  39. 6.01: Ordinary Points
  40. 6.02: Regular Singular Points - Cauchy-Euler Equations
  41. 07: Systems of Equations
  42. 7.01: Matrices Determinants and the Eigenvalue Problem
  43. 7.02: Coupled First-Order Equations
  44. 7.03: Normal Modes
  45. 08: Nonlinear Differential Equations
  46. 8.01: Fixed Points and Stability
  47. 8.02: One-Dimensional Bifurcations
  48. 8.03: Two-Dimensional Bifurcations
  49. 09: Partial Differential Equations
  50. 9.01: Derivation of the Diffusion Equation
  51. 9.02: Derivation of the Wave Equation
  52. 9.03: Fourier Series
  53. 9.04: Fourier Sine and Cosine Series
  54. 9.05: Solution of the Diffusion Equation
  55. 9.06: Solution of the Wave Equation
  56. 9.07: The Laplace Equation
  57. 9.08: The Schrodinger Equation