Math 420: Differential Equations

by Ron Breitenbach

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This text is written for students in science, engineering, and mathematics who have completed single variable calculus. This course will cover the theory and the applications of the solutions of ordinary differential equations and systems of ordinary differential equations. The course will introduce students to various topics useful in the solution of differential equations including power series, Laplace transforms, matrices, eigenvalues and eigenvectors, and numerical methods.

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Publisher
Cosumnes 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: Basic Concepts
  8. 1.1E: Basic Concepts (Exercises)
  9. 1.2: Existence and Uniqueness of Solutions
  10. 1.2E: Existence and Uniqueness of Solutions (Exercises)
  11. 1.3: Direction Fields
  12. 1.3E: Direction Fields (Exercises)
  13. 2: First Order Equations
  14. 2.1: Separable Equations
  15. 2.1E: Separable Equations (Exercises)
  16. 2.2: Exact Equations
  17. 2.2E: Exact Equations (Exercises)
  18. 2.3: Linear First Order Equations
  19. 2.3E: Linear First Order Equations (Exercises)
  20. 2.4: Solving Differential Equations by Substitutions
  21. 2.4E: Solving Differential Equations by Substitution (Exercises)
  22. 3: Numerical Methods
  23. 3.1: Euler's Method
  24. 3.1E: Euler’s Method (Exercises)
  25. 3.2: The Improved Euler Method
  26. 3.2E: The Improved Euler Method (Exercises)
  27. 3.3: The Runge-Kutta Method
  28. 3.3E: The Runge-Kutta Method (Exercises)
  29. 4: Applications of First Order Equations
  30. 4.1: Growth and Decay
  31. 4.1E: Growth and Decay (Exercises)
  32. 4.2: Cooling and Mixing
  33. 4.2E: Cooling and Mixing (Exercises)
  34. 4.3: Elementary Mechanics
  35. 4.3E: Elementary Mechanics (Exercises)
  36. 5: Linear Second Order Equations
  37. 5.1: Homogeneous Linear Equations
  38. 5.1.1: Homogeneous Linear Equations (Exercises)
  39. 5.2: Reduction of Order
  40. 5.2.1: Reduction of Order (Exercises)
  41. 5.3: Constant Coefficient Homogeneous Equations
  42. 5.3.1: Constant Coefficient Homogeneous Equations (Exercises)
  43. 5.4: Nonhomogeneous Linear Equations
  44. 5.4.1: Nonhomgeneous Linear Equations (Exercises)
  45. 5.5: Annihilation
  46. 5.5.1: Annihilation (Exercises)
  47. 5.6: Variation of Parameters
  48. 5.6.1: Variation of Parameters (Exercises)
  49. 5.7: Cauchy-Euler Equations
  50. 5.7.1: Cauchy-Euler Equations (Exercises)
  51. 6: Applications of Linear Second Order Equations
  52. 6.1: Spring-Mass Problems (Without Damping)
  53. 6.1E: Spring-Mass Problems (Without Damping) (Exercises)
  54. 6.2: Spring-Mass Problems (with Damping)
  55. 6.2E: Spring-Mass Problems (With Damping) (Exercises)
  56. 6.3: The RLC Circuit
  57. 6.3E: The RLC Circuit (Exercises)
  58. 7: Linear Higher Order Differential Equations
  59. 7.1: Introduction to Linear Higher Order Equations
  60. 7.1.1: Introduction to Linear Higher Order Equations (Exercises)
  61. 7.2: Higher Order Homogeneous Equations
  62. 7.2.1: Higher Order Homogeneous Equations (Exercises)
  63. 7.3: Annihilation for Higher Order Equations
  64. 7.3.1: Annihilation for Higher Order Equations (Exercises)
  65. 7.4: Variation of Parameters for Higher Order Equations
  66. 7.4.1: Variation of Parameters for Higher Order Equations (Exercises)
  67. 8: Series Solutions of Linear Second Order Equations
  68. 8.1: Prelude to Series Solutions of Linear Second Order Equations
  69. 8.2: Review of Power Series
  70. 8.2.1: Review of Power Series (Exercises)
  71. 8.3: Series Solutions About an Ordinary Point
  72. 8.3.1: Series Solutions About an Ordinary Point (Exercises)
  73. 8.4: Series Solutions About a Regular Singular Point
  74. 8.4.1: Series Solutions About a Regular Singular Point (Exercises)
  75. 9: Laplace Transforms
  76. 9.1: Introduction to the Laplace Transform
  77. 9.1.1: Introduction to the Laplace Transform (Exercises)
  78. 9.2: The Inverse Laplace Transform
  79. 9.2.1: The Inverse Laplace Transform (Exercises)
  80. 9.3: Solutions of Initial Value Problems
  81. 9.3.1: Solution of Initial Value Problems (Exercises)
  82. 9.4: The First Shifting Theorem
  83. 9.4.1: The First Shifting Theorem (Exercises)
  84. 9.5: The Second Shifting Theorem and Piecewise Continuous Forcing Functions
  85. 9.5.1: The Second Shifting Theorem and Piecewise Continuous Forcing Functions (Exercises)
  86. 9.6: Convolution and Periodic Functions
  87. 9.6.1: Convolution and Periodic Functions (Exercises)
  88. 10: Linear Systems of Differential Equations
  89. 10.1: Linear Systems of Differential Equations
  90. 10.1: Linear Systems of Differential Equations (Exercises)
  91. 10.2: Basic Theory of Homogeneous Linear Systems
  92. 10.2.1: Basic Theory of Homogeneous Linear Systems (Exercises)
  93. 10.3: Constant Coefficient Homogeneous Systems I
  94. 10.3.1: Constant Coefficient Homogeneous Systems I (Exercises)
  95. 10.4: Constant Coefficient Homogeneous Systems II
  96. 10.4.1: Constant Coefficient Homogeneous Systems II (Exercises)
  97. 10.5: Constant Coefficient Homogeneous Systems III
  98. 10.5.1: Constant Coefficient Homogeneous Systems III (Exercises)
  99. 10.6: Variation of Parameters for Nonhomogeneous Linear Systems
  100. 10.6.1: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  101. 11: Appendices
  102. 11.1: Functions of Several Variables
  103. 11.1: Functions of Several Variables (Exercises)
  104. 11.2: Partial Derivatives
  105. 11.2.1: Partial Derivatives (Exercises)
  106. 11.3: Determinants and Cramer's Rule for 2 X 2 Matrices
  107. 11.3.1: Determinants and Cramer's Rule for 2 X 2 Matrices (Exercises)
  108. 11.4: Determinants and Cramer's Rule for n x n Matrices
  109. 11.4.1: Determinants and Cramer's Rule for n x n Matrices (Exercises)
  110. 11.5: Elementary Row Operations and Gaussian Elimination
  111. 11.5.1: Elementary Row Operations and Gaussian Elimination (Exercises)
  112. 11.6: Eigenvalues and Eigenvectors
  113. 11.6.1: Eigenvalues and Eigenvectors (Exercises)
  114. 11.7: A Brief Table of Integrals
  115. 11.8: A Brief Table of Trigonometric Identities and Logarithmic Laws
  116. 12: Answers to Exercises and Index
  117. 1: Section 1.1 Answers
  118. 2: Section 1.2 Answers
  119. 3: Section 1.3 Answers
  120. 4: Section 2.1 Answers
  121. 5: Section 2.2 Answers
  122. 6: Section 2.3 Answers
  123. 7: Section 2.4 Answers
  124. 8: Section 3.1 Answers
  125. 9: Section 3.2 Answers
  126. 10: Section 3.3 Answers
  127. 11: Section 4.1 Answers
  128. 12: Section 4.2 Answers
  129. 13: Section 4.3 Answers
  130. 14: Section 5.1 Answers
  131. 15: Section 5.2 Answers
  132. 16: Section 5.3 Answers
  133. 17: Section 5.4 Answers
  134. 18: Section 5.5 Answers
  135. 19: Section 5.6 Answers
  136. 20: Section 5.7 Answers
  137. 21: Section 6.1 Answers
  138. 22: Section 6.2 Answers
  139. 23: Section 6.3 Answers
  140. 24: Section 7.1 Answers
  141. 25: Section 7.2 Answers
  142. 26: Section 7.3 Answers
  143. 27: Section 7.4 Answers
  144. 28: Section 8.2 Answers
  145. 29: Section 8.3 Answers
  146. 30: Section 8.4 Answers
  147. 31: Section 9.1 Answers
  148. 32: Section 9.2 Answers
  149. 33: Section 9.3 Answers
  150. 34: Section 9.4 Answers
  151. 35: Section 9.5 Answers
  152. 36: Section 9.6 Answers
  153. 37: Section 10.1 Answers
  154. 38: Section 10.2 Answers
  155. 39: Section 10.3 Answers
  156. 40: Section 10.4 Answers
  157. 41: Section 10.5 Answers
  158. 42: Section 10.6 Answers
  159. 43: Index
  160. Back Matter
  161. Index
  162. Glossary
  163. Detailed Licensing