Elementary Differential Equations with Boundary Values Problems

by William F. Trench

Read here Read at LibreTextsPDF

This text is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. This book is intended to serve as the book for students in MAT 266 Differential Equations with Linear Algebra at Community College of Denver.

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

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  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: Linear First Order Equations
  14. 2.1E: Linear First Order Equations (Exercises)
  15. 2.2: Separable Equations
  16. 2.2E: Separable 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. 3: Numerical Methods
  26. 3.1: Euler's Method
  27. 3.1E: Euler’s Method (Exercises)
  28. 3.2: The Improved Euler Method and Related Methods
  29. 3.2E: The Improved Euler Method and Related Methods (Exercises)
  30. 3.3: The Runge-Kutta Method
  31. 3.3E: The Runge-Kutta Method (Exercises)
  32. 4: Applications of First Order Equations
  33. 4.1: Growth and Decay
  34. 4.1E: Growth and Decay (Exercises)
  35. 4.2: Cooling and Mixing
  36. 4.2E: Cooling and Mixing (Exercises)
  37. 4.3: Elementary Mechanics
  38. 4.3E: Elementary Mechanics (Exercises)
  39. 4.4: Autonomous Second Order Equations
  40. 4.4E: Autonomous Second Order Equations (Exercises)
  41. 4.5: Applications to Curves
  42. 4.5E: Applications to Curves (Exercises)
  43. 5: Linear Second Order Equations
  44. 5.1: Homogeneous Linear Equations
  45. 5.1E: Homogeneous Linear Equations (Exercises)
  46. 5.2: Constant Coefficient Homogeneous Equations
  47. 5.2E: Constant Coefficient Homogeneous Equations (Exercises)
  48. 5.3: Nonhomogeneous Linear Equations
  49. 5.3E: Nonhomgeneous Linear Equations (Exercises)
  50. 5.4: The Method of Undetermined Coefficients I
  51. 5.4E: The Method of Undetermined Coefficients I (Exercises)
  52. 5.5: The Method of Undetermined Coefficients II
  53. 5.5E: The Method of Undetermined Coefficients II (Exercises)
  54. 5.6: Reduction of Order
  55. 5.6E: Reduction of Order (Exercises)
  56. 5.7: Variation of Parameters
  57. 5.7E: Variation of Parameters (Exercises)
  58. 6: Applications of Linear Second Order Equations
  59. 6.1: Spring Problems I
  60. 6.1E: Spring Problems I (Exercises)
  61. 6.2: Spring Problems II
  62. 6.2E: Spring Problems II (Exercises)
  63. 7: Series Solutions of Linear Second Order Equations
  64. 7.1: Review of Power Series
  65. 7.1E: Review of Power Series (Exercises)
  66. 7.2: Series Solutions Near an Ordinary Point I
  67. 7.2E: Series Solutions Near an Ordinary Point I (Exercises)
  68. 7.3: Series Solutions Near an Ordinary Point II
  69. 7.3E: Series Solutions Near an Ordinary Point II (Exercises)
  70. Prelude to Series Solutions of Linear Second Order Equations
  71. 8: Laplace Transforms
  72. 8.1: Introduction to the Laplace Transform
  73. 8.1E: Introduction to the Laplace Transform (Exercises)
  74. 8.2: The Inverse Laplace Transform
  75. 8.2E: The Inverse Laplace Transform (Exercises)
  76. 8.3: Solution of Initial Value Problems
  77. 8.3E: Solution of Initial Value Problems (Exercises)
  78. 8.4: A Brief Table of Laplace Transforms
  79. 9: Linear Higher Order Differential Equations
  80. 9.1: Introduction to Linear Higher Order Equations
  81. 9.1E: Introduction to Linear Higher Order Equations (Exercises)
  82. 9.2: Higher Order Constant Coefficient Homogeneous Equations
  83. 9.2E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  84. 9.3: Undetermined Coefficients for Higher Order Equations
  85. 9.3E: Undetermined Coefficients for Higher Order Equations (Exercises)
  86. 9.4: Variation of Parameters for Higher Order Equations
  87. 9.4E: Variation of Parameters for Higher Order Equations (Exercises)
  88. 10: Linear Systems of Differential Equations
  89. 10.1: Introduction to Systems of Differential Equations
  90. 10.1E: Introduction to Systems of Differential Equations (Exercises)
  91. 10.2: Linear Systems of Differential Equations
  92. 10.2E: Linear Systems of Differential Equations (Exercises)
  93. 10.3: Basic Theory of Homogeneous Linear Systems
  94. 10.3E: Basic Theory of Homogeneous Linear Systems (Exercises)
  95. 10.4: Constant Coefficient Homogeneous Systems I
  96. 10.4E: Constant Coefficient Homogeneous Systems I (Exercises)
  97. 10.5: Constant Coefficient Homogeneous Systems II
  98. 10.5E: Constant Coefficient Homogeneous Systems II (Exercises)
  99. 10.6: Constant Coefficient Homogeneous Systems III
  100. 10.6E: Constant Coefficient Homogeneous Systems III (Exercises)
  101. 11: Systems of Equations
  102. 11.1: Geometry
  103. 11.2: Elementary Operations
  104. 11.3: Gaussian Elimination
  105. 11.E: Exercises
  106. 12: Matrices and Determinants
  107. 12.1: Matrix Arithmetic
  108. 12.2: Multiplication of Matrices
  109. 12.3: The ijth Entry of a Product
  110. 12.4: Properties of Matrix Multiplication
  111. 12.5: The Transpose
  112. 12.6: The Identity and Inverses
  113. 12.7: Finding the Inverse of a Matrix
  114. 12.8: Basic Techniques of Determinants
  115. 12.9: Properties of Determinants
  116. 12.10: Finding Determinants using Row Operations
  117. 12.E: Exercises
  118. 13: Vector Spaces
  119. 13.1: Algebraic Considerations
  120. 13.2: Spanning Sets
  121. 13.3: Linear Independence
  122. 13.4: Subspaces and Basis
  123. 13.5: Sums and Intersections
  124. 13.6: Linear Transformations
  125. 13.E: Exercises
  126. 14: Appendices and Answers to Exercises
  127. 14.1: A Brief Table of Integrals
  128. 14.2: Index
  129. 14.3: Section 1.2 Answers
  130. 14.4: Section 2.1 Answers
  131. 14.5: Section 2.2 Answers
  132. 14.6: Section 2.3 Answers
  133. 14.7: Section 2.4 Answers
  134. 14.8: Section 2.5 Answers
  135. 14.9: Section 2.6 Answers
  136. 14.10: Section 3.1 Answers
  137. 14.11: Section 3.2 Answers
  138. 14.12: Section 3.3 Answers
  139. 14.13: Section 4.1 Answers
  140. 14.14: Section 4.2 Answers
  141. 14.15: Section 4.3 Answers
  142. 14.16: Section 4.4 Answers
  143. 14.17: Section 4.5 Answers
  144. 14.18: Section 5.1 Answers
  145. 14.19: Section 5.2 Answers
  146. 14.20: Section 5.3 Answers
  147. 14.21: Section 5.4 Answers
  148. 14.22: Section 5.5 Answers
  149. 14.23: Section 5.6 Answers
  150. 14.24: Section 5.7 Answers
  151. 14.25: Section 6.1 Answers
  152. 14.26: Section 6.2 Answers
  153. 14.27: Section 6.3 Answers
  154. 14.28: Section 6.4 Answers
  155. 14.29: Section 7.1 Answers
  156. 14.30: Section 7.2 Answers
  157. 14.31: Section 7.3 Answers
  158. 14.32: Section 7.4 Answers
  159. 14.33: Section 7.5 Answers
  160. 14.34: Section 7.6 Answers
  161. 14.35: Section 7.7 Answers
  162. 14.36: Section 8.1 Answers
  163. 14.37: Section 8.2 Answers
  164. 14.38: Section 8.3 Answers
  165. 14.39: Section 8.4 Answers
  166. 14.40: Section 8.5 Answers
  167. 14.41: Section 8.6 Answers
  168. 14.42: Section 8.7 Answers
  169. 14.43: Section 9.1 Answers
  170. 14.44: Section 9.2 Answers
  171. 14.45: Section 9.3 Answers
  172. 14.46: Section 9.4 Answers
  173. 14.47: Section 10.1 Answers
  174. 14.48: Section 10.2 Answers
  175. 14.49: Section 10.3 Answers
  176. 14.50: Section 10.4 Answers
  177. 14.51: Section 10.5 Answers
  178. 14.52: Section 10.6 Answers
  179. 14.53: Section 10.7 Answers
  180. Back Matter
  181. Index
  182. Glossary
  183. Glossary
  184. Detailed Licensing