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Math 4: Differential Equations (Dinh)

This is a typical course on elementary differential equations, which can be taken after two semesters of single variable calculus. Topics include first, second and higher order equations, Laplace transforms, series solution and applications.

Mathematics
Tác giả
Hung Dinh
Nhà xuất bản
Chabot College
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LibreTexts
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EN
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Mục lục· 130 mục
  1. 01: Introduction
  2. 1.01: Introduction to Differential Equations
  3. 1.02: Applications Leading to Differential Equations
  4. 1.03: Basic Concepts
  5. 1.3E: Basic Concepts (Exercises)
  6. 1.04: Direction Fields for First Order Equations
  7. 1.4.01: Direction Fields for First Order Equations (Exercises)
  8. 02: First Order Equations
  9. 2.01: Linear First Order Equations (Option 1- Variation of Parameters)
  10. 2.1E: Linear First Order Equations (Exercises)
  11. 2.02: Linear First Order Equations (Option 2- Integrating Factors)
  12. 2.03: Separable Equations
  13. 2.3E: Separable Equations (Exercises)
  14. 2.04: Existence and Uniqueness of Solutions of Nonlinear Equations
  15. 2.4E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  16. 2.05: Transformation of Nonlinear Equations into Separable Equations
  17. 2.5E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  18. 2.06: Exact Equations
  19. 2.6E: Exact Equations (Exercises)
  20. 2.07: Integrating Factors
  21. 2.7E: Integrating Factors (Exercises)
  22. 03: Applications of First Order Equations
  23. 3.01: Growth and Decay
  24. 3.1E: Growth and Decay (Exercises)
  25. 3.02: Cooling and Mixing
  26. 3.2E: Cooling and Mixing (Exercises)
  27. 3.03: Elementary Mechanics
  28. 3.3E: Elementary Mechanics (Exercises)
  29. 3.04: Autonomous Second Order Equations
  30. 3.4E: Autonomous Second Order Equations (Exercises)
  31. 3.05: Applications to Curves
  32. 3.5E: Applications to Curves (Exercises)
  33. 04: Linear Higher Order Differential Equations
  34. 4.01: Second Order Homogeneous Linear Equations
  35. 4.1E: Homogeneous Linear Equations (Exercises)
  36. 4.02: Introduction to Linear Higher Order Equations
  37. 4.2E: Introduction to Linear Higher Order Equations (Exercises)
  38. 4.03: Second Order Constant Coefficient Homogeneous Equations
  39. 4.3E: Constant Coefficient Homogeneous Equations (Exercises)
  40. 4.04: Higher Order Constant Coefficient Homogeneous Equations
  41. 4.4E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  42. 4.05: Second Order Nonhomogeneous Linear Equations (Polynomial Forcing)
  43. 4.5E: Nonhomgeneous Linear Equations (Exercises)
  44. 4.06: Undetermined Coefficients for Second Order Equations (Exponential Forcing)
  45. 4.6E: The Method of Undetermined Coefficients I (Exercises)
  46. 4.07: Undetermined Coefficients for Second Order Equations (Trigonometry Forcing)
  47. 4.7E: The Method of Undetermined Coefficients II (Exercises)
  48. 4.08: Undetermined Coefficients for Higher Order Equations
  49. 4.8E: Undetermined Coefficients for Higher Order Equations (Exercises)
  50. 4.09: Reduction of Order
  51. 4.9E: Reduction of Order (Exercises)
  52. 4.10: Variation of Parameters for Second Order Equations
  53. 4.10E: Variation of Parameters (Exercises)
  54. 4.11: Variation of Parameters for Higher Order Equations
  55. 4.11E: Variation of Parameters for Higher Order Equations (Exercises)
  56. 05: Applications of Linear Second Order Equations
  57. 5.01: Spring Problems (Undamped Motion)
  58. 5.1E: Spring Problems I (Exercises)
  59. 5.02: Spring Problems (Damped Motion)
  60. 5.2E: Spring Problems II (Exercises)
  61. 5.03: The RLC Circuit
  62. 5.3E: The RLC Circuit (Exercises)
  63. 5.04: Motion Under a Central Force
  64. 5.4E: Motion Under a Central Force (Exercises)
  65. 06: Laplace Transforms
  66. 6.01: Introduction to the Laplace Transform
  67. 6.1E: Introduction to the Laplace Transform (Exercises)
  68. 6.02: The Inverse Laplace Transform
  69. 6.2E: The Inverse Laplace Transform (Exercises)
  70. 6.03: Solution of Initial Value Problems
  71. 6.3E: Solution of Initial Value Problems (Exercises)
  72. 6.04: The Unit Step Function
  73. 6.4E: The Unit Step Function (Exercises)
  74. 6.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  75. 6.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  76. 6.06: Convolution
  77. 6.6E: Convolution (Exercises)
  78. 6.07: Constant Coefficient Equations with Impulses
  79. 6.7E: Constant Coefficient Equations with Impulses (Exercises)
  80. 6.08: A Brief Table of Laplace Transforms
  81. 07: Series Solutions of Linear Second Order Equations
  82. 7.01: Prelude to Series Solutions of Linear Second Order Equations
  83. 7.02: Review of Power Series
  84. 7.2E: Review of Power Series (Exercises)
  85. 7.03: Series Solutions Near an Ordinary Point I
  86. 7.3E: Series Solutions Near an Ordinary Point I (Exercises)
  87. 7.04: Series Solutions Near an Ordinary Point II
  88. 7.4E: Series Solutions Near an Ordinary Point II (Exercises)
  89. 7.05: Regular Singular Points Euler Equations
  90. 7.5E: Regular Singular Points Euler Equations (Exercises)
  91. 7.06: The Method of Frobenius I
  92. 7.6E: The Method of Frobenius I (Exercises)
  93. 7.07: The Method of Frobenius II
  94. 7.7E: The Method of Frobenius II (Exercises)
  95. 7.08: The Method of Frobenius III
  96. 7.8E: The Method of Frobenius III (Exercises)
  97. 08: Linear Systems of Differential Equations
  98. 8.01: Introduction to Systems of Differential Equations
  99. 8.1E: Introduction to Systems of Differential Equations (Exercises)
  100. 8.02: Linear Systems of Differential Equations
  101. 8.2E: Linear Systems of Differential Equations (Exercises)
  102. 8.03: Basic Theory of Homogeneous Linear Systems
  103. 8.3E: Basic Theory of Homogeneous Linear Systems (Exercises)
  104. 8.04: Constant Coefficient Homogeneous Systems I
  105. 8.4E: Constant Coefficient Homogeneous Systems I (Exercises)
  106. 8.05: Constant Coefficient Homogeneous Systems II
  107. 8.5E: Constant Coefficient Homogeneous Systems II (Exercises)
  108. 8.06: Constant Coefficient Homogeneous Systems III
  109. 8.6E: Constant Coefficient Homogeneous Systems III (Exercises)
  110. 8.07: Variation of Parameters for Nonhomogeneous Linear Systems
  111. 8.7E: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  112. 09: Appendices
  113. 9.01: A Short Review
  114. 9.1.01: The Trigonometric Functions
  115. 9.1.02: The Exponential Function and the Natural Logarithm
  116. 9.1.03: Definition of the Derivative
  117. 9.1.04: Differentiating a Combination of Functions
  118. 9.1.05: Differentiating Elementary Functions
  119. 9.1.06: Definition of the Integral
  120. 9.1.07: The Fundamental Theorem of Calculus
  121. 9.1.08: Definite and Indefinite Integrals
  122. 9.1.09: Indefinite Integrals of Elementary Functions
  123. 9.1.10: Substitution
  124. 9.1.11: Integration by Parts
  125. 9.1.12: Taylor Series
  126. 9.1.13: Functions of Several Variables
  127. 9.1.14: Complex Numbers
  128. 9.02: Solving Systems with Cramer's Rule
  129. 9.2E: Solving Systems with Cramer's Rule (Exercises)
  130. 9.03: Partial Fractions