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Differential Equations and Linear Algebra

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Differential Equations and Linear Algebra

This text is intended for engineering, science, and math majors who have completed a three semester calculus sequence.

Mathematics
Author
Steven Zook
Publisher
Reedley College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 133 sections
  1. 01: Systems of Equations
  2. 1.01: Systems of Equations Geometry
  3. 1.02: Systems of Equations Algebraic Procedures
  4. 1.03: Gaussian Elimination
  5. 1.04: Uniqueness of the Reduced Row-Echelon Form
  6. 1.05: Rank and Homogeneous Systems
  7. 1.06: Exercises
  8. 02: Matrices
  9. 2.01: Matrix Arithmetic
  10. 2.02: Multiplication of Matrices
  11. 2.03: The ijth Entry of a Product
  12. 2.04: Properties of Matrix Multiplication
  13. 2.05: The Transpose
  14. 2.06: The Identity and Inverses
  15. 2.07: Finding the Inverse of a Matrix
  16. 2.08: Elementary Matrices
  17. 2.09: More on Matrix Inverses
  18. 2.10: LU Factorization
  19. 2.11: Exercises
  20. 03: Determinants
  21. 3.01: Basic Techniques
  22. 3.02: Properties of Determinants
  23. 3.03: Finding Determinants using Row Operations
  24. 3.04: Applications of the Determinant
  25. 3.05: Exercises
  26. 04: R
  27. 4.01: Vectors in R
  28. 4.02: Vector Algebra
  29. 4.03: Geometric Meaning of Vector Addition
  30. 4.04: Length of a Vector
  31. 4.05: Geometric Meaning of Scalar Multiplication
  32. 4.06: Parametric Lines
  33. 4.07: Spanning Linear Independence and Basis in R
  34. 4.08: Orthogonality
  35. 4.09: Applications
  36. 4.10: Exercises
  37. 05: Linear Transformations
  38. 5.01: Linear Transformations
  39. 5.02: The Matrix of a Linear Transformation I
  40. 5.03: Properties of Linear Transformations
  41. 5.04: Special Linear Transformations in R
  42. 5.05: One-to-One and Onto Transformations
  43. 5.06: The Kernel and Image of A Linear Map
  44. 5.07: The Matrix of a Linear Transformation II
  45. 5.08: The General Solution of a Linear System
  46. 5.09: Exercises
  47. 06: Spectral Theory
  48. 6.01: Eigenvalues and Eigenvectors of a Matrix
  49. 6.02: Diagonalization
  50. 6.03: Applications of Spectral Theory
  51. 6.04: Orthogonality
  52. 6.05: Exercises
  53. 07: What are Differential Equations
  54. 7.01: Applications Leading to Differential Equations
  55. 7.02: Basic Concepts
  56. 7.2.01: Basic Concepts (Exercises)
  57. 7.03: Direction Fields for First Order Equations
  58. 7.3.01: Direction Fields for First Order Equations (Exercises)
  59. 08: First Order Equations
  60. 8.01: Linear First Order Equations
  61. 8.1.01: Linear First Order Equations (Exercises)
  62. 8.02: Separable Equations
  63. 8.2.01: Separable Equations (Exercises)
  64. 8.03: Existence and Uniqueness of Solutions of Nonlinear Equations
  65. 8.3.01: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  66. 8.04: Transformation of Nonlinear Equations into Separable Equations
  67. 8.4.01: Transformation of Nonlinear Equations into Separable Equations (Exercises)
  68. 8.05: Exact Equations
  69. 8.5.01: Exact Equations (Exercises)
  70. 8.06: Integrating Factors
  71. 8.6.01: Integrating Factors (Exercises)
  72. 09: Applications of First Order Equations
  73. 9.01: Growth and Decay
  74. 9.1.01: Growth and Decay (Exercises)
  75. 9.02: Cooling and Mixing
  76. 9.2.01: Cooling and Mixing (Exercises)
  77. 9.03: Elementary Mechanics
  78. 9.3.01: Elementary Mechanics (Exercises)
  79. 10: Linear Second Order Equations
  80. 10.01: Homogeneous Linear Equations
  81. 10.1.01: Homogeneous Linear Equations (Exercises)
  82. 10.02: Constant Coefficient Homogeneous Equations
  83. 10.2.01: Constant Coefficient Homogeneous Equations (Exercises)
  84. 10.03: Nonhomogeneous Linear Equations
  85. 10.3.01: Nonhomgeneous Linear Equations (Exercises)
  86. 10.04: The Method of Undetermined Coefficients I
  87. 10.4.01: The Method of Undetermined Coefficients I (Exercises)
  88. 10.05: The Method of Undetermined Coefficients II
  89. 10.5.01: The Method of Undetermined Coefficients II (Exercises)
  90. 10.06: Reduction of Order
  91. 10.6.01: Reduction of Order (Exercises)
  92. 11: Applications of Linear Second Order Equations
  93. 11.01: Spring Problems I
  94. 11.1.01: Spring Problems I (Exercises)
  95. 11.02: Spring Problems II
  96. 11.2.01: Spring Problems II (Exercises)
  97. 12: Series Solutions of Linear Second Order Equations
  98. 12.01: Prelude to Series Solutions of Linear Second Order Equations
  99. 12.02: Review of Power Series
  100. 12.2.01: Review of Power Series (Exercises)
  101. 12.03: Series Solutions Near an Ordinary Point I
  102. 12.3.01: Series Solutions Near an Ordinary Point I (Exercises)
  103. 13: Laplace Transforms
  104. 13.01: Introduction to the Laplace Transform
  105. 13.1.01: Introduction to the Laplace Transform (Exercises)
  106. 13.02: The Inverse Laplace Transform
  107. 13.2.01: The Inverse Laplace Transform (Exercises)
  108. 13.03: Solution of Initial Value Problems
  109. 13.3.01: Solution of Initial Value Problems (Exercises)
  110. 13.04: The Unit Step Function
  111. 13.4.01: The Unit Step Function (Exercises)
  112. 13.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  113. 13.5.01: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  114. 13.06: A Brief Table of Laplace Transforms
  115. 14: Linear Higher Order Differential Equations
  116. 14.01: Introduction to Linear Higher Order Equations
  117. 14.1.01: Introduction to Linear Higher Order Equations (Exercises)
  118. 14.02: Higher Order Constant Coefficient Homogeneous Equations
  119. 14.2.01: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
  120. 15: Linear Systems of Differential Equations
  121. 15.01: Introduction to Systems of Differential Equations
  122. 15.1.01: Introduction to Systems of Differential Equations (Exercises)
  123. 15.02: Linear Systems of Differential Equations
  124. 15.2.01: Linear Systems of Differential Equations (Exercises)
  125. 15.03: Basic Theory of Homogeneous Linear Systems
  126. 15.3.01: Basic Theory of Homogeneous Linear Systems (Exercises)
  127. 15.04: Constant Coefficient Homogeneous Systems I
  128. 15.4.01: Constant Coefficient Homogeneous Systems I (Exercises)
  129. 16: Appendices
  130. 16.01: Trigonometric Identities
  131. 16.02: Review of Derivative Rules
  132. 16.03: Table of Derivatives
  133. 16.04: Table of Integrals