Introductory Differential Equations

by Vinh Kha Nguyen, Neelam R. Shukla & Fatemeh Yarahmadi

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

Description from LibreTexts.

Publisher
De Anza College
Subjects
Mathematics
Licence
CC BY-NC-SA 3.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Program Page
  5. Table of Contents
  6. Licensing
  7. About the Book
  8. About the Authors
  9. 1: First Order ODEs
  10. 1.1: Introduction to Differential Equations
  11. 1.1E: Exercises for Section 1.1
  12. 1.2: Classification of Differential Equations
  13. 1.2E: Exercises for Section 1.2
  14. 1.3: Integrals as Solutions
  15. 1.3E: Exercises for Section 1.3
  16. 1.4: Slope Fields
  17. 1.4E: Exercises for Section 1.4
  18. 1.5: Separable Equations
  19. 1.5E: Exercises for Section 1.5
  20. 1.6: Linear Equations and the Integrating Factor
  21. 1.6E: Exercises for the section 1.6
  22. 1.7: Existence and Uniqueness of Solutions of Nonlinear Equations
  23. 1.7E: Exercises for the section 1.7
  24. 1.8: Substitution
  25. 1.8E: Exercises for Section 1.8
  26. 1.9: Autonomous Equations
  27. 1.9E: Exercises for Section 1.9
  28. 1.10: Numerical Methods - Euler’s Method
  29. 1.10E: Exercises for Section 1.10
  30. 1.11: Exact Equations
  31. 1.11E: Exercises for Section 1.11
  32. 1.12: Transformation of Nonlinear Equations into Separable Equations
  33. 1.12E: Exercises for Section 1.12
  34. 2: Applications of First Order Equations
  35. 2.1: Growth and Decay
  36. 2.1E: Exercises for Section 2.1
  37. 2.2: Cooling Problems
  38. 2.2E: Exercises for Section 2.2
  39. 2.3: Elementary Mechanics
  40. 2.3E: Exercises for Section 2.3
  41. 2.4: Mixing Problems
  42. 2.4E: Exercises for Section 2.4
  43. 2.5: Orthogonal Trajectories of Curves and Pursuit Curves
  44. 2.5E: Exercises for Section 2.5
  45. 3: Higher order linear ODEs
  46. 3.1: Second order linear ODEs
  47. 3.1E: Exercises for Section 3.1
  48. 3.2: The Method of Undetermined Coefficients I
  49. 3.2E: Exercises for Section 3.2
  50. 3.3: The Method of Undetermined Coefficients II
  51. 3.3E: Exercises for Section 3.3
  52. 3.4: Constant coefficient second order linear ODEs
  53. 3.4E: Exercises for Section 3.4
  54. 3.5: Higher order linear ODEs
  55. 3.5E: Exercises for Section 3.5
  56. 3.6: Reduction of Order
  57. 3.6E: Exercises for Section 3.6
  58. 3.7: Variation of Parameters
  59. 3.7E: Exercises for Section 3.7
  60. 3.8: Mechanical Vibrations
  61. 3.8E: Exercises for Section 3.8
  62. 3.9: Nonhomogeneous Equations
  63. 3.9E: Exercises for Section 3.9
  64. 3.10: Forced Oscillations and Resonance
  65. 3.10E: Exercises for Section 3.10
  66. 4: Power series methods
  67. 4.1: Power Series
  68. 4.1E: Exercises for Section 4.1
  69. 4.2: Series Solutions of Linear Second Order ODEs
  70. 4.2E: Exercises for Section 4.2
  71. 4.3: Singular Points and the Method of Frobenius
  72. 4.3E: Exercises for Section 4.3
  73. 5: The Laplace Transform
  74. 5.1: The Laplace Transform
  75. 5.1E: Exercises for Section 5.1
  76. 5.2: Transforms of Derivatives and ODEs
  77. 5.2E: Exercises for Section 5.2
  78. 5.3: Convolution
  79. 5.3E: Exercises for Section 5.3
  80. 6: Systems of ODEs
  81. 6.1: Introduction to Systems of ODEs
  82. 6.1E: Exercises for Section 6.1
  83. 6.2: Linear Systems of ODEs
  84. 6.2E: Exercises for Section 6.2
  85. 6.3: Eigenvalue Method
  86. 6.3E: Exercises for Section 6.3
  87. Back Matter
  88. Index
  89. Glossary
  90. Detailed Licensing
  91. Detailed Licensing