Elementary Differential Equations with Boundary Values Problems

by William F. Trench

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This text is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

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Publisher
Trinity University
Subjects
Mathematics, Differential Equations
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. Preface
  7. 1: Introduction
  8. 1.1: Applications Leading to Differential Equations
  9. 1.2: Basic Concepts
  10. 1.2E: Basic Concepts (Exercises)
  11. 1.3: Direction Fields for First Order Equations
  12. 1.3E: Direction Fields for First Order Equations (Exercises)
  13. 2: First Order Equations
  14. 2.1: Linear First Order Equations
  15. 2.1E: Linear First Order Equations (Exercises)
  16. 2.2: Separable Equations
  17. 2.2E: Separable Equations (Exercises)
  18. 2.3: Existence and Uniqueness of Solutions of Nonlinear Equations
  19. 2.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  20. 2.4: Transformation of Nonlinear Equations into Separable Equations
  21. 2.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  22. 2.5: Exact Equations
  23. 2.5E: Exact Equations (Exercises)
  24. 2.6: Integrating Factors
  25. 2.6E: Integrating Factors (Exercises)
  26. 3: Numerical Methods
  27. 3.1: Euler's Method
  28. 3.1E: Euler’s Method (Exercises)
  29. 3.2: The Improved Euler Method and Related Methods
  30. 3.2E: The Improved Euler Method and Related Methods (Exercises)
  31. 3.3: The Runge-Kutta Method
  32. 3.3E: The Runge-Kutta Method (Exercises)
  33. 4: Applications of First Order Equations
  34. 4.1: Growth and Decay
  35. 4.1E: Growth and Decay (Exercises)
  36. 4.2: Cooling and Mixing
  37. 4.2E: Cooling and Mixing (Exercises)
  38. 4.3: Elementary Mechanics
  39. 4.3E: Elementary Mechanics (Exercises)
  40. 4.4: Autonomous Second Order Equations
  41. 4.4E: Autonomous Second Order Equations (Exercises)
  42. 4.5: Applications to Curves
  43. 4.5E: Applications to Curves (Exercises)
  44. 5: Linear Second Order Equations
  45. 5.1: Homogeneous Linear Equations
  46. 5.1E: Homogeneous Linear Equations (Exercises)
  47. 5.2: Constant Coefficient Homogeneous Equations
  48. 5.2E: Constant Coefficient Homogeneous Equations (Exercises)
  49. 5.3: Nonhomogeneous Linear Equations
  50. 5.3E: Nonhomgeneous Linear Equations (Exercises)
  51. 5.4: The Method of Undetermined Coefficients I
  52. 5.4E: The Method of Undetermined Coefficients I (Exercises)
  53. 5.5: The Method of Undetermined Coefficients II
  54. 5.5E: The Method of Undetermined Coefficients II (Exercises)
  55. 5.6: Reduction of Order
  56. 5.6E: Reduction of Order (Exercises)
  57. 5.7: Variation of Parameters
  58. 5.7E: Variation of Parameters (Exercises)
  59. 6: Applications of Linear Second Order Equations
  60. 6.1: Spring Problems I
  61. 6.1E: Spring Problems I (Exercises)
  62. 6.2: Spring Problems II
  63. 6.2E: Spring Problems II (Exercises)
  64. 6.3: The RLC Circuit
  65. 6.3E: The RLC Circuit (Exercises)
  66. 6.4: Motion Under a Central Force
  67. 6.4E: Motion Under a Central Force (Exercises)
  68. 7: Series Solutions of Linear Second Order Equations
  69. 7.1: Prelude to Series Solutions of Linear Second Order Equations
  70. 7.2: Review of Power Series
  71. 7.2E: Review of Power Series (Exercises)
  72. 7.3: Series Solutions Near an Ordinary Point I
  73. 7.3E: Series Solutions Near an Ordinary Point I (Exercises)
  74. 7.4: Series Solutions Near an Ordinary Point II
  75. 7.4E: Series Solutions Near an Ordinary Point II (Exercises)
  76. 7.5: Regular Singular Points Euler Equations
  77. 7.5E: Regular Singular Points Euler Equations (Exercises)
  78. 7.6: The Method of Frobenius I
  79. 7.6E: The Method of Frobenius I (Exercises)
  80. 7.7: The Method of Frobenius II
  81. 7.7E: The Method of Frobenius II (Exercises)
  82. 7.8: The Method of Frobenius III
  83. 7.8E: The Method of Frobenius III (Exercises)
  84. 8: Laplace Transforms
  85. 8.1: Introduction to the Laplace Transform
  86. 8.1E: Introduction to the Laplace Transform (Exercises)
  87. 8.2: The Inverse Laplace Transform
  88. 8.2E: The Inverse Laplace Transform (Exercises)
  89. 8.3: Solution of Initial Value Problems
  90. 8.3E: Solution of Initial Value Problems (Exercises)
  91. 8.4: The Unit Step Function
  92. 8.4E: The Unit Step Function (Exercises)
  93. 8.5: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  94. 8.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  95. 8.6: Convolution
  96. 8.6E: Convolution (Exercises)
  97. 8.7: Constant Coefficient Equations with Impulses
  98. 8.7E: Constant Coefficient Equations with Impulses (Exercises)
  99. 8.8: A Brief Table of Laplace Transforms
  100. 9: Linear Higher Order Differential Equations
  101. 9.1: Introduction to Linear Higher Order Equations
  102. 9.1E: Introduction to Linear Higher Order Equations (Exercises)
  103. 9.2: Higher Order Constant Coefficient Homogeneous Equations
  104. 9.2E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  105. 9.3: Undetermined Coefficients for Higher Order Equations
  106. 9.3E: Undetermined Coefficients for Higher Order Equations (Exercises)
  107. 9.4: Variation of Parameters for Higher Order Equations
  108. 9.4E: Variation of Parameters for Higher Order Equations (Exercises)
  109. 10: Linear Systems of Differential Equations
  110. 10.1: Introduction to Systems of Differential Equations
  111. 10.1E: Introduction to Systems of Differential Equations (Exercises)
  112. 10.2: Linear Systems of Differential Equations
  113. 10.2E: Linear Systems of Differential Equations (Exercises)
  114. 10.3: Basic Theory of Homogeneous Linear Systems
  115. 10.3E: Basic Theory of Homogeneous Linear Systems (Exercises)
  116. 10.4: Constant Coefficient Homogeneous Systems I
  117. 10.4E: Constant Coefficient Homogeneous Systems I (Exercises)
  118. 10.5: Constant Coefficient Homogeneous Systems II
  119. 10.5E: Constant Coefficient Homogeneous Systems II (Exercises)
  120. 10.6: Constant Coefficient Homogeneous Systems III
  121. 10.6E: Constant Coefficient Homogeneous Systems III (Exercises)
  122. 10.7: Variation of Parameters for Nonhomogeneous Linear Systems
  123. 10.7E: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
  124. 11: Boundary Value Problems and Fourier Expansions
  125. 11.1: Eigenvalue Problems for y'' + λy = 0
  126. 11.1E: Eigenvalue Problems for y'' + λy = 0 (Exercises)
  127. 11.2: Fourier Series I
  128. 11.2E: Fourier Series I (Exercises)
  129. 11.3: Fourier Series II
  130. 11.3E: Fourier Series II (Exercises)
  131. 12: Fourier Solutions of Partial Differential Equations
  132. 12.1: The Heat Equation
  133. 12.1E: The Heat Equation (Exercises)
  134. 12.2: The Wave Equation
  135. 12.2E: The Wave Equation (Exercises)
  136. 12.3: Laplace's Equation in Rectangular Coordinates
  137. 12.3E: Laplace's Equation in Rectangular Coordinates (Exercises)
  138. 12.4: Laplace's Equation in Polar Coordinates
  139. 12.4E: Laplace's Equation in Polar Coordinates (Exercises)
  140. 13: Boundary Value Problems for Second Order Linear Equations
  141. 13.1: Boundary Value Problems
  142. 13.1E: Boundary Value Problems (Exercises)
  143. 13.2: Sturm-Liouville Problems
  144. 13.2E: Sturm-Liouville Problems (Exercises)
  145. A: Appendices and Answers to Exercises
  146. A.1.2: Section 1.2 Answers
  147. A.2.1: Section 2.1 Answers
  148. A.2.2: Section 2.2 Answers
  149. A.2.3: Section 2.3 Answers
  150. A.2.4: Section 2.4 Answers
  151. A.2.5: Section 2.5 Answers
  152. A.2.6: Section 2.6 Answers
  153. A.3.1: Section 3.1 Answers
  154. A.3.2: Section 3.2 Answers
  155. A.3.3: Section 3.3 Answers
  156. A.4.1: Section 4.1 Answers
  157. A.4.2: Section 4.2 Answers
  158. A.4.3: Section 4.3 Answers
  159. A.4.4: Section 4.4 Answers
  160. A.4.5: Section 4.5 Answers
  161. A.5.1: Section 5.1 Answers
  162. A.5.2: Section 5.2 Answers
  163. A.5.3: Section 5.3 Answers
  164. A.5.4: Section 5.4 Answers
  165. A.5.5: Section 5.5 Answers
  166. A.5.6: Section 5.6 Answers
  167. A.5.7: Section 5.7 Answers
  168. A.6.1: Section 6.1 Answers
  169. A.6.2: Section 6.2 Answers
  170. A.6.3: Section 6.3 Answers
  171. A.6.4: Section 6.4 Answers
  172. A.7.1: Section 7.1 Answers
  173. A.7.2: Section 7.2 Answers
  174. A.7.3: Section 7.3 Answers
  175. A.7.4: Section 7.4 Answers
  176. A.7.5: Section 7.5 Answers
  177. A.7.6: Section 7.6 Answers
  178. A.7.7: Section 7.7 Answers
  179. A.8.1: Section 8.1 Answers
  180. A.8.2: Section 8.2 Answers
  181. A.8.3: Section 8.3 Answers
  182. A.8.4: Section 8.4 Answers
  183. A.8.5: Section 8.5 Answers
  184. A.8.6: Section 8.6 Answers
  185. A.8.7: Section 8.7 Answers
  186. A.9.1: Section 9.1 Answers
  187. A.9.2: Section 9.2 Answers
  188. A.9.3 Section 9.3 Answers
  189. A.9.4: Section 9.4 Answers
  190. A.10.1: Section 10.1 Answers
  191. A.10.2 Section 10.2 Answers
  192. A.10.3: Section 10.3 Answers
  193. A.10.4 Section 10.4 Answers
  194. A.10.5: Section 10.5 Answers
  195. A.10.6 Section 10.6 Answers
  196. A.10.7: Section 10.7 Answers
  197. A.11.1: Section 11.1 Answers
  198. A.11.2: Section 11.2 Answers
  199. A.11.3: Section 11.3 Answers
  200. A.12.1: Section 12.1 Answers
  201. A.12.2: Section 12.2 Answers
  202. A.12.3: Section 12.3 Answers
  203. A.12.4: Section 12.4 Answers
  204. A.13.1: Section 13.1 Answers
  205. A.13.2: Section 13.2 Answers
  206. A Brief Table of Integrals (by Trench)
  207. Index
  208. Back Matter
  209. Index
  210. Detailed Licensing