Math 4B: Differential Equations

by Zoya Kravets

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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.

Description from LibreTexts.

Publisher
Mission 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. Table of Contents
  5. Licensing
  6. 1: Introduction
  7. 1.1: Applications Leading to Differential Equations
  8. 1.2: Basic Concepts
  9. 1.2E: Basic Concepts (Exercises)
  10. 1.3: Direction Fields for First Order Equations
  11. 1.3E: Direction Fields for First Order Equations (Exercises)
  12. 2: First Order Equations
  13. 2.1: Separable Equations
  14. 2.1E: Separable Equations (Exercises)
  15. 2.2: Linear First Order Equations
  16. 2.2E: Linear First Order Equations (Exercises)
  17. 2.3: Existence and Uniqueness of Solutions of Nonlinear Equations
  18. 2.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  19. 2.4: Transformation of Nonlinear Equations into Separable Equations
  20. 2.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  21. 2.5: Exact Equations
  22. 2.5E: Exact Equations (Exercises)
  23. 2.6: Integrating Factors
  24. 2.6E: Integrating Factors (Exercises)
  25. 2.7: Euler's Method
  26. 2.7E: Euler’s Method (Exercises)
  27. 3: Applications of First Order Equations
  28. 3.1: Growth and Decay
  29. 3.1E: Growth and Decay (Exercises)
  30. 3.2: Elementary Mechanics
  31. 3.2E: Elementary Mechanics (Exercises)
  32. 3.3: Autonomous Second Order Equations
  33. 3.3E: Autonomous Second Order Equations (Exercises)
  34. 4: Linear Second Order Equations
  35. 4.1: Homogeneous Linear Equations
  36. 4.1E: Homogeneous Linear Equations (Exercises)
  37. 4.2: Introduction to Linear Higher Order Equations
  38. 4.2E: Introduction to Linear Higher Order Equations (Exercises)
  39. 4.3: Constant Coefficient Homogeneous Equations
  40. 4.3E: Constant Coefficient Homogeneous Equations (Exercises)
  41. 4.4: Higher Order Constant Coefficient Homogeneous Equations
  42. 4.4E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  43. 4.5: Nonhomgeneous Linear Equations
  44. 4.5E: Nonhomgeneous Linear Equations (Exercises)
  45. 4.6: The Method of Undetermined Coefficients I
  46. 4.6E: The Method of Undetermined Coefficients I (Exercises)
  47. 4.7: The Method of Undetermined Coefficients II
  48. 4.7E: The Method of Undetermined Coefficients II (Exercises)
  49. 4.8: Undetermined Coefficients for Higher Order Equations
  50. 4.8E: Undetermined Coefficients for Higher Order Equations (Exercises)
  51. 4.9: Reduction of Order
  52. 4.9E: Reduction of Order (Exercises)
  53. 4.10: Variation of Parameters
  54. 4.10E: Variation of Parameters (Exercises)
  55. 4.11: Variation of Parameters for Higher Order Equations
  56. 4.11E: Variation of Parameters for Higher Order Equations (Exercises)
  57. 5: Applications of Linear Second Order Equations
  58. 5.1: Spring Problems I
  59. 5.1E: Spring Problems I (Exercises)
  60. 5.2: Spring Problems II
  61. 5.2E: Spring Problems II (Exercises)
  62. 5.3: The RLC Circuit
  63. 5.3E: The RLC Circuit (Exercises)
  64. 6: Series Solutions of Linear Second Order Equations
  65. 6.1: Prelude to Series Solutions of Linear Second Order Equations
  66. 6.2: Review of Power Series
  67. 6.2.1: Review of Power Series (Exercises)
  68. 6.3: Series Solutions Near an Ordinary Point I
  69. 6.3.1: Series Solutions Near an Ordinary Point I (Exercises)
  70. 6.4: Regular Singular Points Euler Equations
  71. 6.4.1: Regular Singular Points Euler Equations (Exercises)
  72. 6.5: The Method of Frobenius I
  73. 6.5.1: The Method of Frobenius I (Exercises)
  74. 6.6: The Method of Frobenius II
  75. 6.6.1: The Method of Frobenius II (Exercises)
  76. 6.7: The Method of Frobenius III
  77. 6.7.1: The Method of Frobenius III (Exercises)
  78. 7: Laplace Transforms
  79. 7.1: Introduction to the Laplace Transform
  80. 7.1E: Introduction to the Laplace Transform (Exercises)
  81. 7.2: The Inverse Laplace Transform
  82. 7.2E: The Inverse Laplace Transform (Exercises)
  83. 7.3: Solution of Initial Value Problems
  84. 7.3E: Solution of Initial Value Problems (Exercises)
  85. 7.4: The Unit Step Function
  86. 7.4E: The Unit Step Function (Exercises)
  87. 7.5: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  88. 7.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  89. 7.6: Convolution
  90. 7.6E: Convolution (Exercises)
  91. 7.7: A Brief Table of Laplace Transforms
  92. 8: Boundary Value Problems and Fourier Expansions
  93. 8.1: Eigenvalue Problems for y'' + λy = 0
  94. 8.1E: Eigenvalue Problems for y'' + λy = 0 (Exercises)
  95. 8.2: Fourier Series I
  96. 8.2E: Fourier Series I (Exercises)
  97. 8.3: Fourier Series II
  98. 8.3E: Fourier Series II (Exercises)
  99. 9: Fourier Solutions of Partial Differential Equations
  100. 9.1: The Heat Equation
  101. 9.1E: The Heat Equation (Exercises)
  102. 9.2: The Wave Equation
  103. 9.2E: The Wave Equation (Exercises)
  104. 10: Linear Systems of Differential Equations
  105. 10.1: Introduction to Systems of Differential Equations
  106. 10.1E: Introduction to Systems of Differential Equations (Exercises)
  107. Back Matter
  108. Index
  109. Index
  110. Glossary
  111. Detailed Licensing