MTH 225 Differential Equations

by William F. Trench

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A standard course in ordinary differential equations that includes both qualitative and analytic methods.

Description from LibreTexts.

Publisher
Trinity University
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. 1: Introduction
  2. 1.1: Applications Leading to Differential Equations
  3. 1.2: Basic Concepts
  4. 1.2E: Basic Concepts (Exercises)
  5. 1.3: Direction Fields for First Order Equations
  6. 1.3E: Direction Fields for First Order Equations (Exercises)
  7. 2: First Order Equations
  8. 2.1: Linear First Order Equations
  9. 2.1.1: Linear First Order Equations (Exercises)
  10. 2.2: Separable Equations
  11. 2.2.1: Separable Equations (Exercises)
  12. 2.3: Existence and Uniqueness of Solutions of Nonlinear Equations
  13. 2.3.1: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  14. 2.4: Bifurcations
  15. 2.5: Substitution Methods - Transformation of Nonlinear Equations into Separable Equations
  16. 2.5.1: Substitution Methods - Transformation of Nonlinear Equations into Separable Equations (Exercises)
  17. 2.6: Exact Equations
  18. 2.6.1: Exact Equations (Exercises)
  19. 2.7: Using Multiple Integrating Factors
  20. 2.7.1: Using Multiple Integrating Factors (Exercises)
  21. 3: Numerical Methods
  22. 3.1: Euler's Method
  23. 3.1.1: Euler’s Method (Exercises)
  24. 3.2: The Improved Euler Method and Related Methods
  25. 3.2.1: The Improved Euler Method and Related Methods (Exercises)
  26. 3.3: The Runge-Kutta Method
  27. 3.3.1: The Runge-Kutta Method (Exercises)
  28. 4: Applications of First Order Equations
  29. 4.1: Growth and Decay
  30. 4.1.1: Growth and Decay (Exercises)
  31. 4.2: Cooling and Mixing
  32. 4.2.1: Cooling and Mixing (Exercises)
  33. 4.3: Elementary Mechanics
  34. 4.3.1: Elementary Mechanics (Exercises)
  35. 4.4: Autonomous Second Order Equations
  36. 4.4.1: Autonomous Second Order Equations (Exercises)
  37. 4.5: Applications to Curves
  38. 4.5.1: Applications to Curves (Exercises)
  39. 5: Linear Second Order Equations
  40. 5.1: Homogeneous Linear Equations
  41. 5.1.1: Homogeneous Linear Equations (Exercises)
  42. 5.2: Constant Coefficient Homogeneous Equations
  43. 5.2.1: Constant Coefficient Homogeneous Equations (Exercises)
  44. 5.3: Nonhomgeneous Linear Equations
  45. 5.3.1: Nonhomgeneous Linear Equations (Exercises)
  46. 5.4: The Method of Undetermined Coefficients I
  47. 5.4.1: The Method of Undetermined Coefficients I (Exercises)
  48. 5.5: The Method of Undetermined Coefficients II
  49. 5.5.1: The Method of Undetermined Coefficients II (Exercises)
  50. 5.6: Reduction of Order
  51. 5.6.1: Reduction of Order (Exercises)
  52. 5.7: Variation of Parameters
  53. 5.7.1: Variation of Parameters (Exercises)
  54. 6: Applications of Linear Second Order Equations
  55. 6.1: Spring Problems I
  56. 6.1.1: Spring Problems I (Exercises)
  57. 6.2: Spring Problems II
  58. 6.2.1: Spring Problems II (Exercises)
  59. 6.3: The RLC Circuit
  60. 6.3.1: The RLC Circuit (Exercises)
  61. 6.4: Motion Under a Central Force
  62. 6.4.1: Motion Under a Central Force (Exercises)
  63. 7: Series Solutions of Linear Second Order Equations
  64. 7.0: Prelude to Series Solutions of Linear Second Order Equations
  65. 7.1: Review of Power Series
  66. 7.1.1: Review of Power Series (Exercises)
  67. 7.2: Series Solutions Near an Ordinary Point I
  68. 7.2E: Series Solutions Near an Ordinary Point I (Exercises)
  69. 7.3: Series Solutions Near an Ordinary Point II
  70. 7.3.1: Series Solutions Near an Ordinary Point II (Exercises)
  71. 7.4: Regular Singular Points Euler Equations
  72. 7.4.1: Regular Singular Points Euler Equations (Exercises)
  73. 7.5: The Method of Frobenius I
  74. 7.5.1: The Method of Frobenius I (Exercises)
  75. 7.6: The Method of Frobenius II
  76. 7.6.1: The Method of Frobenius II (Exercises)
  77. 7.7: The Method of Frobenius III
  78. 7.7.1: The Method of Frobenius III (Exercises)
  79. 8: Laplace Transforms
  80. 8.1: Introduction to the Laplace Transform
  81. 8.1.1: Introduction to the Laplace Transform (Exercises)
  82. 8.2: The Inverse Laplace Transform
  83. 8.2.1: The Inverse Laplace Transform (Exercises)
  84. 8.3: Solution of Initial Value Problems
  85. 8.3.1: Solution of Initial Value Problems (Exercises)
  86. 8.4: The Unit Step Function
  87. 8.4.1: The Unit Step Function (Exercises)
  88. 8.5: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  89. 8.5.1: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  90. 8.6: Convolution
  91. 8.6.1: Convolution (Exercises)
  92. 8.7: Constant Coefficient Equations with Impulses
  93. 8.7.1: Constant Coefficient Equations with Impulses (Exercises)
  94. A Brief Table of Laplace Transforms (Trench's)
  95. Professor Seeburger's Table of Laplace Transforms
  96. 9: Linear Higher Order Differential Equations
  97. 9.1: Introduction to Linear Higher Order Equations
  98. 9.1.1: Introduction to Linear Higher Order Equations (Exercises)
  99. 9.2: Higher Order Constant Coefficient Homogeneous Equations
  100. 9.2.1: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  101. 9.3: Undetermined Coefficients for Higher Order Equations
  102. 9.3.1: Undetermined Coefficients for Higher Order Equations (Exercises)
  103. 9.4: Variation of Parameters for Higher Order Equations
  104. 9.4.1: Variation of Parameters for Higher Order Equations (Exercises)
  105. 10: Linear Systems of Differential Equations
  106. 10.1: Introduction to Systems of Differential Equations
  107. 10.1.1: Introduction to Systems of Differential Equations (Exercises)
  108. 10.2: Linear Systems of Differential Equations
  109. 10.2.1: Linear Systems of Differential Equations (Exercises)
  110. 10.3: Basic Theory of Homogeneous Linear Systems
  111. 10.3.1: Basic Theory of Homogeneous Linear Systems (Exercises)
  112. 10.4: Constant Coefficient Homogeneous Systems I
  113. 10.4.1: Constant Coefficient Homogeneous Systems I (Exercises)
  114. 10.5: Constant Coefficient Homogeneous Systems II
  115. 10.5.1: Constant Coefficient Homogeneous Systems II (Exercises)
  116. 10.6: Constant Coefficient Homogeneous Systems III
  117. 10.6.1: Constant Coefficient Homogeneous Systems III (Exercises)
  118. 10.7: Variation of Parameters for Nonhomogeneous Linear Systems
  119. 10.7.1: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  120. 11: Answers to Selected Exercises
  121. 11.1: A.1.2- Section 1.2 Answers
  122. 11.2: A.10.1- Section 10.1 Answers
  123. 11.3: A.10.2 Section 10.2 Answers
  124. 11.4: A.10.3- Section 10.3 Answers
  125. 11.5: A.10.4 Section 10.4 Answers
  126. 11.6: A.10.5- Section 10.5 Answers
  127. 11.7: A.10.6 Section 10.6 Answers
  128. 11.8: A.10.7- Section 10.7 Answers
  129. 11.9: A.11.1- Section 11.1 Answers
  130. 11.10: A.11.2- Section 11.2 Answers
  131. 11.11: A.11.3- Section 11.3 Answers
  132. 11.12: A.12.1- Section 12.1 Answers
  133. 11.13: A.12.2- Section 12.2 Answers
  134. 11.14: A.12.3- Section 12.3 Answers
  135. 11.15: A.12.4- Section 12.4 Answers
  136. 11.16: A.13.1- Section 13.1 Answers
  137. 11.17: A.13.2- Section 13.2 Answers
  138. 11.18: A.2.1- Section 2.1 Answers
  139. 11.19: A.2.2- Section 2.2 Answers
  140. 11.20: A.2.3- Section 2.3 Answers
  141. 11.21: A.2.4- Section 2.4 Answers
  142. 11.22: A.2.5- Section 2.5 Answers
  143. 11.23: A.2.6- Section 2.6 Answers
  144. 11.24: A.3.1- Section 3.1 Answers
  145. 11.25: A.3.2- Section 3.2 Answers
  146. 11.26: A.3.3- Section 3.3 Answers
  147. 11.27: A.4.1- Section 4.1 Answers
  148. 11.28: A.4.2- Section 4.2 Answers
  149. 11.29: A.4.3- Section 4.3 Answers
  150. 11.30: A.4.4- Section 4.4 Answers
  151. 11.31: A.4.5- Section 4.5 Answers
  152. 11.32: A.5.1- Section 5.1 Answers
  153. 11.33: A.5.2- Section 5.2 Answers
  154. 11.34: A.5.3- Section 5.3 Answers
  155. 11.35: A.5.4- Section 5.4 Answers
  156. 11.36: A.5.5- Section 5.5 Answers
  157. 11.37: A.5.6- Section 5.6 Answers
  158. 11.38: A.5.7- Section 5.7 Answers
  159. 11.39: A.6.1- Section 6.1 Answers
  160. 11.40: A.6.2- Section 6.2 Answers
  161. 11.41: A.6.3- Section 6.3 Answers
  162. 11.42: A.6.4- Section 6.4 Answers
  163. 11.43: A.7.1- Section 7.1 Answers
  164. 11.44: A.7.2- Section 7.2 Answers
  165. 11.45: A.7.3- Section 7.3 Answers
  166. 11.46: A.7.4- Section 7.4 Answers
  167. 11.47: A.7.5- Section 7.5 Answers
  168. 11.48: A.7.6- Section 7.6 Answers
  169. 11.49: A.7.7- Section 7.7 Answers
  170. 11.50: A.8.1- Section 8.1 Answers
  171. 11.51: A.8.2- Section 8.2 Answers
  172. 11.52: A.8.3- Section 8.3 Answers
  173. 11.53: A.8.4- Section 8.4 Answers
  174. 11.54: A.8.5- Section 8.5 Answers
  175. 11.55: A.8.6- Section 8.6 Answers
  176. 11.56: A.8.7- Section 8.7 Answers
  177. 11.57: A.9.1- Section 9.1 Answers
  178. 11.58: A.9.2- Section 9.2 Answers
  179. 11.59: A.9.3 Section 9.3 Answers
  180. 11.60: A.9.4- Section 9.4 Answers
  181. 11.61: A Brief Table of Integrals (by Trench)
  182. 11.62: A Brief Table of Integrals (edited by Prof. Seeburger)
  183. 11.63: Index