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Introduction to Differential Equations (IVC Math 24)

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Introduction to Differential Equations (IVC Math 24)

This textbook covers a first course in ordinary differential equations, including first order (linear and non-linear), higher order linear differential equations, Laplace Transformations, power series solutions, and a wide array of real-world applications.

Mathematics
Author
Kenn Huber
Publisher
Irvine Valley College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 101 sections
  1. 01: First Order Differential Equations
  2. 1.01: Integration Review
  3. 1.1.01: Integration Review
  4. 1.1.02: Practice Set
  5. 1.02: Basic Terminology
  6. 1.2.01: Linear Algebra Review
  7. 1.2.02: Differential Equation Terminology
  8. 1.2.03: Practice Set
  9. 1.03: Partial Derivatives and Exact Equations
  10. 1.3.01: Partial Differentiation and Integration
  11. 1.3.02: Exact Equations
  12. 1.3.03: Practice Set
  13. 1.04: Separable Equations and Existence Theorem
  14. 1.4.01: Picard's Existence Theorem
  15. 1.4.02: Separable Differential Equations
  16. 1.4.03: Practice Set
  17. 1.05: First Order Linear Differential Equations
  18. 1.5.01: Solving Linear Differential Equations
  19. 1.5.02: Practice Set
  20. 1.06: Substitutions
  21. 1.6.01: Substitution In Differential Equations
  22. 1.6.02: Famous DEs and Their Substitutions
  23. 1.6.03: Practice Set
  24. 02: Higher Order Linear Differential Equations
  25. 2.01: Independent Solutions
  26. 2.1.01: Higher Order LDE Solution Sets
  27. 2.1.02: Practice Set
  28. 2.02: Constant Coeffecient and Cauchy Euler LDEs
  29. 2.2.01: Constant Coeffecient LDEs
  30. 2.2.02: Cauchy Euler LDEs
  31. 2.2.03: Practice Set
  32. 2.03: Reduction of Order
  33. 2.3.01: Reduction of Order in 2nd Order LDEs
  34. 2.3.02: Practice Set
  35. 2.04: Undetermined Coefficients
  36. 2.4.01: Guessing Solutions
  37. 2.4.02: Practice Set
  38. 2.05: Variation of Parameters
  39. 2.5.01: Varation of Parameters for 2nd order LDEs
  40. 2.5.02: Practice Set
  41. 2.06: Systems of LDEs
  42. 2.6.01: Solving Linear Systems of LDEs
  43. 2.6.02: Practice Set
  44. 03: Laplace Transformations
  45. 3.01: The Laplace Transformation
  46. 3.1.01: Laplace Transformation Basics
  47. 3.1.02: The Inverse Laplace Transformation
  48. 3.1.03: Practice Set
  49. 3.02: Laplace Derivative Properties
  50. 3.2.01: Differentiation of Outputs of Laplace
  51. 3.2.02: Differentiation of Inputs of Laplace
  52. 3.2.03: Practice Set
  53. 3.03: Piecewise Differential Equations
  54. 3.3.01: Piecewise Functions and the Unit Step Function
  55. 3.3.02: Laplace Transformations of Piecewise Functions
  56. 3.3.03: Practice Set
  57. 3.04: Integro-Differential Equations
  58. 3.4.01: Convolutions and Laplace
  59. 3.4.02: Practice Set
  60. 3.05: Dirac Delta
  61. 3.5.01: The Dirac Delta Function
  62. 3.5.02: Practice Set
  63. 3.06: Systems of Differential Equations Revisited
  64. 3.6.01: Solving Systems using Laplace
  65. 3.6.02: Practice Set
  66. 04: Power Series Methods and Approximations
  67. 4.01: Power Series
  68. 4.1.01: Power Series Review
  69. 4.1.02: Practice Set
  70. 4.02: First order LDE Power Series solutions
  71. 4.2.01: Power Series Solutions
  72. 4.2.02: Practice Set
  73. 4.03: Second Order Power Series Solutions
  74. 4.3.01: Second Order Power Series Solutions
  75. 4.3.02: Practice Set
  76. 4.04: Power Series Solutions at Singular Points
  77. 4.4.01: The Method of Frobenius and Indicial Equation
  78. 4.4.02: Distinct Power Series Solutions using Frobenius Method
  79. 4.4.03: Frobenius Method (bad cases)
  80. 4.4.04: Practice Set
  81. 4.05: Approximating Solutions
  82. 4.5.01: Euler's Method
  83. 4.5.02: Runge-Kutta Approximation
  84. 4.5.03: Power Series Approximation
  85. 4.5.04: Practice Set
  86. 05: Applications
  87. 5.01: Applications of First Order Differential Equations
  88. 5.1.01: Separable Models
  89. 5.1.02: Practice Set
  90. 5.02: Orthogonal Curves
  91. 5.2.01: Orthogonal Trajectories
  92. 5.2.02: Practice Set
  93. 5.03: Mixtures
  94. 5.3.01: Mixture Problems
  95. 5.3.02: Practice Set
  96. 5.04: Hooke's Law
  97. 5.4.01: Springs
  98. 5.4.02: Practice Set
  99. 5.05: Circuits
  100. 5.5.01: RLC Circuits and External Forces
  101. 5.5.02: Practice Set