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Introductory Differential Equations

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Introductory Differential Equations

Topics in the course include methods of solving ordinary differential equations and selected applications.

Mathematics
Author
Vinh Kha Nguyen, Neelam R. Shukla & Fatemeh Yarahmadi
Publisher
De Anza College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 78 sections
  1. 01: First Order ODEs
  2. 1.01: Introduction to Differential Equations
  3. 1.1E: Exercises for Section 1.1
  4. 1.02: Classification of Differential Equations
  5. 1.2E: Exercises for Section 1.2
  6. 1.03: Integrals as Solutions
  7. 1.3E: Exercises for Section 1.3
  8. 1.04: Slope Fields
  9. 1.4E: Exercises for Section 1.4
  10. 1.05: Separable Equations
  11. 1.5E: Exercises for Section 1.5
  12. 1.06: Linear Equations and the Integrating Factor
  13. 1.6E: Exercises for the section 1.6
  14. 1.07: Existence and Uniqueness of Solutions of Nonlinear Equations
  15. 1.7E: Exercises for the section 1.7
  16. 1.08: Substitution
  17. 1.8E: Exercises for Section 1.8
  18. 1.09: Autonomous Equations
  19. 1.9E: Exercises for Section 1.9
  20. 1.10: Numerical Methods - Eulers Method
  21. 1.10E: Exercises for Section 1.10
  22. 1.11: Exact Equations
  23. 1.11E: Exercises for Section 1.11
  24. 1.12: Transformation of Nonlinear Equations into Separable Equations
  25. 1.12E: Exercises for Section 1.12
  26. 02: Applications of First Order Equations
  27. 2.01: Growth and Decay
  28. 2.1E: Exercises for Section 2.1
  29. 2.02: Cooling Problems
  30. 2.2E: Exercises for Section 2.2
  31. 2.03: Elementary Mechanics
  32. 2.3E: Exercises for Section 2.3
  33. 2.04: Mixing Problems
  34. 2.4E: Exercises for Section 2.4
  35. 2.05: Orthogonal Trajectories of Curves and Pursuit Curves
  36. 2.5E: Exercises for Section 2.5
  37. 03: Higher order linear ODEs
  38. 3.01: Second order linear ODEs
  39. 3.1E: Exercises for Section 3.1
  40. 3.02: The Method of Undetermined Coefficients I
  41. 3.2E: Exercises for Section 3.2
  42. 3.03: The Method of Undetermined Coefficients II
  43. 3.3E: Exercises for Section 3.3
  44. 3.04: Constant coefficient second order linear ODEs
  45. 3.4E: Exercises for Section 3.4
  46. 3.05: Higher order linear ODEs
  47. 3.5E: Exercises for Section 3.5
  48. 3.06: Reduction of Order
  49. 3.6E: Exercises for Section 3.6
  50. 3.07: Variation of Parameters
  51. 3.7E: Exercises for Section 3.7
  52. 3.08: Mechanical Vibrations
  53. 3.8E: Exercises for Section 3.8
  54. 3.09: Nonhomogeneous Equations
  55. 3.9E: Exercises for Section 3.9
  56. 3.10: Forced Oscillations and Resonance
  57. 3.10E: Exercises for Section 3.10
  58. 04: Power series methods
  59. 4.01: Power Series
  60. 4.1E: Exercises for Section 4.1
  61. 4.02: Series Solutions of Linear Second Order ODEs
  62. 4.2E: Exercises for Section 4.2
  63. 4.03: Singular Points and the Method of Frobenius
  64. 4.3E: Exercises for Section 4.3
  65. 05: The Laplace Transform
  66. 5.01: The Laplace Transform
  67. 5.1E: Exercises for Section 5.1
  68. 5.02: Transforms of Derivatives and ODEs
  69. 5.2E: Exercises for Section 5.2
  70. 5.03: Convolution
  71. 5.3E: Exercises for Section 5.3
  72. 06: Systems of ODEs
  73. 6.01: Introduction to Systems of ODEs
  74. 6.1E: Exercises for Section 6.1
  75. 6.02: Linear Systems of ODEs
  76. 6.2E: Exercises for Section 6.2
  77. 6.03: Eigenvalue Method
  78. 6.3E: Exercises for Section 6.3