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Introductory Differential Equations

Nguồn ngoài

Introductory Differential Equations

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

Mathematics
Tác giả
Vinh Kha Nguyen, Neelam R. Shukla & Fatemeh Yarahmadi
Nhà xuất bản
De Anza College
Nguồn
LibreTexts
Giấy phép
CC BY-NC-SA
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 78 mục
  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