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Math 4B: Differential Equations

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Math 4B: Differential Equations

Topics include ordinary differential equations, with emphasis on linear equations, and partial differential equations. Methods include Laplace Transforms, power series, Fourier series, numerical solutions and applications.

Mathematics
Author
Zoya Kravets
Publisher
Mission College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 101 sections
  1. 01: Introduction
  2. 1.01: Applications Leading to Differential Equations
  3. 1.02: Basic Concepts
  4. 1.2E: Basic Concepts (Exercises)
  5. 1.03: Direction Fields for First Order Equations
  6. 1.3E: Direction Fields for First Order Equations (Exercises)
  7. 02: First Order Equations
  8. 2.01: Separable Equations
  9. 2.1E: Separable Equations (Exercises)
  10. 2.02: Linear First Order Equations
  11. 2.2E: Linear First Order Equations (Exercises)
  12. 2.03: Existence and Uniqueness of Solutions of Nonlinear Equations
  13. 2.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  14. 2.04: Transformation of Nonlinear Equations into Separable Equations
  15. 2.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  16. 2.05: Exact Equations
  17. 2.5E: Exact Equations (Exercises)
  18. 2.06: Integrating Factors
  19. 2.6E: Integrating Factors (Exercises)
  20. 2.07: Euler's Method
  21. 2.7E: Eulers Method (Exercises)
  22. 03: Applications of First Order Equations
  23. 3.01: Growth and Decay
  24. 3.1E: Growth and Decay (Exercises)
  25. 3.02: Elementary Mechanics
  26. 3.2E: Elementary Mechanics (Exercises)
  27. 3.03: Autonomous Second Order Equations
  28. 3.3E: Autonomous Second Order Equations (Exercises)
  29. 04: Linear Second Order Equations
  30. 4.01: Homogeneous Linear Equations
  31. 4.1E: Homogeneous Linear Equations (Exercises)
  32. 4.02: Introduction to Linear Higher Order Equations
  33. 4.2E: Introduction to Linear Higher Order Equations (Exercises)
  34. 4.03: Constant Coefficient Homogeneous Equations
  35. 4.3E: Constant Coefficient Homogeneous Equations (Exercises)
  36. 4.04: Higher Order Constant Coefficient Homogeneous Equations
  37. 4.4E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  38. 4.05: Nonhomgeneous Linear Equations
  39. 4.5E: Nonhomgeneous Linear Equations (Exercises)
  40. 4.06: The Method of Undetermined Coefficients I
  41. 4.6E: The Method of Undetermined Coefficients I (Exercises)
  42. 4.07: The Method of Undetermined Coefficients II
  43. 4.7E: The Method of Undetermined Coefficients II (Exercises)
  44. 4.08: Undetermined Coefficients for Higher Order Equations
  45. 4.8E: Undetermined Coefficients for Higher Order Equations (Exercises)
  46. 4.09: Reduction of Order
  47. 4.9E: Reduction of Order (Exercises)
  48. 4.10: Variation of Parameters
  49. 4.10E: Variation of Parameters (Exercises)
  50. 4.11: Variation of Parameters for Higher Order Equations
  51. 4.11E: Variation of Parameters for Higher Order Equations (Exercises)
  52. 05: Applications of Linear Second Order Equations
  53. 5.01: Spring Problems I
  54. 5.1E: Spring Problems I (Exercises)
  55. 5.02: Spring Problems II
  56. 5.2E: Spring Problems II (Exercises)
  57. 5.03: The RLC Circuit
  58. 5.3E: The RLC Circuit (Exercises)
  59. 06: Series Solutions of Linear Second Order Equations
  60. 6.01: Prelude to Series Solutions of Linear Second Order Equations
  61. 6.02: Review of Power Series
  62. 6.2.01: Review of Power Series (Exercises)
  63. 6.03: Series Solutions Near an Ordinary Point I
  64. 6.3.01: Series Solutions Near an Ordinary Point I (Exercises)
  65. 6.04: Regular Singular Points Euler Equations
  66. 6.4.01: Regular Singular Points Euler Equations (Exercises)
  67. 6.05: The Method of Frobenius I
  68. 6.5.01: The Method of Frobenius I (Exercises)
  69. 6.06: The Method of Frobenius II
  70. 6.6.01: The Method of Frobenius II (Exercises)
  71. 6.07: The Method of Frobenius III
  72. 6.7.01: The Method of Frobenius III (Exercises)
  73. 07: Laplace Transforms
  74. 7.01: Introduction to the Laplace Transform
  75. 7.1E: Introduction to the Laplace Transform (Exercises)
  76. 7.02: The Inverse Laplace Transform
  77. 7.2E: The Inverse Laplace Transform (Exercises)
  78. 7.03: Solution of Initial Value Problems
  79. 7.3E: Solution of Initial Value Problems (Exercises)
  80. 7.04: The Unit Step Function
  81. 7.4E: The Unit Step Function (Exercises)
  82. 7.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  83. 7.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  84. 7.06: Convolution
  85. 7.6E: Convolution (Exercises)
  86. 7.07: A Brief Table of Laplace Transforms
  87. 08: Boundary Value Problems and Fourier Expansions
  88. 8.01: Eigenvalue Problems for y'' y 0
  89. 8.1E: Eigenvalue Problems for y'' y 0 (Exercises)
  90. 8.02: Fourier Series I
  91. 8.2E: Fourier Series I (Exercises)
  92. 8.03: Fourier Series II
  93. 8.3E: Fourier Series II (Exercises)
  94. 09: Fourier Solutions of Partial Differential Equations
  95. 9.01: The Heat Equation
  96. 9.1E: The Heat Equation (Exercises)
  97. 9.02: The Wave Equation
  98. 9.2E: The Wave Equation (Exercises)
  99. 10: Linear Systems of Differential Equations
  100. 10.01: Introduction to Systems of Differential Equations
  101. 10.1E: Introduction to Systems of Differential Equations (Exercises)