Differential Equations (No Linear Algebra Required)

by Marilena Beckstrand, Adam Manriquez & Emad Shonoda

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Publisher
Mt. San Jacinto College
Subjects
Mathematics
Licence
CC BY-NC-SA 4.0, 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 to Differential Equations
  7. 1.1: Introduction to Differential Equations
  8. 1.1E: Introduction to Differential Equations (Exercises)
  9. 1.2: Classification of Differential Equations
  10. 1.2E: Classification of Differential Equations (Exercises)
  11. 1.3: Existence and Uniqueness of Solutions
  12. 1.3E: Existence and Uniqueness of Solutions (Exercises)
  13. 2: First Order Equations
  14. 2.1: Integrals as Solutions
  15. 2.1E: Integrals as Solutions (Exercises)
  16. 2.2: Slope Fields
  17. 2.2E: Slope Fields (Exercises)
  18. 2.3: Separable Equations
  19. 2.3E: Separable Equations (Exercises)
  20. 2.4: First Order Linear Differential Equations
  21. 2.4E: First Order Linear Differential Equations (Exercises)
  22. 2.5: Exact Equations
  23. 2.5E: Exact Equations (Exercises)
  24. 2.6: Substitution
  25. 2.6E: Substitution (Exercises)
  26. 2.7: Numerical Methods- Euler’s Method
  27. 2.7E: Numerical Methods- Euler’s Method (Exercises)
  28. 3: Applications of First Order Equations
  29. 3.1: Growth and Decay
  30. 3.1E: Growth and Decay (Exercises)
  31. 3.2: Cooling and Mixing
  32. 3.2E: Cooling and Mixing (Exercises)
  33. 3.3: Newton's Second Law of Motion
  34. 3.3E: Elementary Mechanics (Exercises)
  35. 4: Higher Order Linear ODEs
  36. 4.1: Homogeneous Linear Second Order Equations
  37. 4.1E: Homogeneous Linear Second Order Equations (Exercises)
  38. 4.2: Nonhomogeneous Linear Second Order Equations
  39. 4.2E: Nonhomogeneous Linear Second Order Equations (Exercises)
  40. 4.3: Reduction of Order
  41. 4.3E: Reduction of Order (Exercises)
  42. 4.4: Homogeneous Linear Second Order Equations with Constant Coefficients
  43. 4.4E: Homogeneous Linear Second Order Equations with Constant Coefficients (Exercises)
  44. 4.5: Homogeneous Linear Higher-Order Differential Equations
  45. 4.5E: Homogeneous Linear Higher-Order Differential Equations (Exercises)
  46. 4.6: Undetermined Coefficients - Annihilator Approach
  47. 4.6E: Undetermined Coefficients - Annihilator Approach (Exercises)
  48. 4.7: Variation of Parameters
  49. 4.7E: Variation of Parameters (Exercises)
  50. 4.8: Cauchy-Euler Equations
  51. 4.8E: Cauchy-Euler Equations (Exercises)
  52. 4.9: Systems of Linear Equations by Systemic Elimination
  53. 4.9E: Systems of Linear Equations by Systemic Elimination (Exercises)
  54. 5: Applications of Second Order Linear Equations
  55. 5.1: Applications of Second-Order Differential Equations
  56. 5.1E: Spring-Mass Problems (Exercises)
  57. 6: Series Solutions of Linear Equations
  58. 6.1: Review of Power Series
  59. 6.1E: Review of Power Series (Exercises)
  60. 6.2: Series Solutions About Ordinary Points
  61. 6.2E: Series Solutions About Ordinary Points (Exercises)
  62. 6.3: Singular Points and the Method of Frobenius
  63. 6.3E: Singular Points and the Method of Frobenius (Exercises)
  64. 7: Laplace Transform
  65. 7.1: Introduction to the Laplace Transform
  66. 7.1E: Introduction to the Laplace Transform (Exercises)
  67. 7.2: The Inverse Laplace Transform
  68. 7.2E: The Inverse Laplace Transform (Exercises)
  69. 7.3: Solution of Initial Value Problems
  70. 7.3E: Solution of Initial Value Problems (Exercises)
  71. 7.4: Derivatives of Laplace Transforms and Linear Models
  72. 7.4E: Derivatives of Laplace Transforms and Linear Models (Exercises)
  73. 7.5: Convolution
  74. 7.5E: Convolution (Exercises)
  75. 8: Appendices
  76. 8.1: Functions of Several Variables
  77. 8.1E: Functions of Several Variables (Exercises)
  78. 8.2: Partial Derivatives
  79. 8.2E: Partial Derivatives (Exercises)
  80. 8.3: Determinants and Cramer's Rule for 2 X 2 Matrices
  81. 8.3E: Determinants and Cramer's Rule for 2 X 2 Matrices (Exercises)
  82. 8.4: A Brief Table of Integrals
  83. 8.5: A Brief Table of Trigonometric Identities and Logarithmic Laws
  84. 8.6: A Brief Table of Laplace Transforms
  85. 9: Answers to Exercises
  86. 9.1: Chapter 1 Answers
  87. 9.2: Chapter 2 Answers
  88. 9.3: Chapter 3 Answers
  89. 9.4: Chapter 4 Answers
  90. 9.5: Chapter 5 Answers
  91. 9.6: Chapter 6 Answers
  92. 9.7: Chapter 7 Answers
  93. 9.8: Table of Contents
  94. Back Matter
  95. Index
  96. Glossary
  97. Detailed Licensing