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Math C285: Linear Algebra and Diffrential Equations (Tran)

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Math C285: Linear Algebra and Diffrential Equations (Tran)

Mathematics
Author
Chau D. Tran
Publisher
Coastline College
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 148 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: Balancing Chemical Reactions
  8. 1.07: Dimensionless Variables
  9. 1.08: An Application to Resistor Networks
  10. 1.09: Exercises
  11. 02: Systems of Equations
  12. 2.01: Systems of Equations Geometry
  13. 2.02: Systems of Equations Algebraic Procedures
  14. 2.03: Gaussian Elimination
  15. 2.04: Uniqueness of the Reduced Row-Echelon Form
  16. 2.05: Rank and Homogeneous Systems
  17. 2.06: Balancing Chemical Reactions
  18. 2.07: Dimensionless Variables
  19. 2.08: An Application to Resistor Networks
  20. 2.09: Exercises
  21. 03: Determinants
  22. 3.01: Basic Techniques
  23. 3.02: Properties of Determinants
  24. 3.03: Finding Determinants using Row Operations
  25. 3.04: Applications of the Determinant
  26. 3.E: Exercises
  27. 04: R
  28. 4.01: Vectors in R
  29. 4.02: Vector Algebra
  30. 4.03: Geometric Meaning of Vector Addition
  31. 4.04: Length of a Vector
  32. 4.05: Geometric Meaning of Scalar Multiplication
  33. 4.06: Parametric Lines
  34. 4.07: The Dot Product
  35. 4.08: Planes in R
  36. 4.09: The Cross Product
  37. 4.10: Spanning Linear Independence and Basis in R
  38. 4.11: Orthogonality
  39. 4.12: Applications
  40. 4.E: Exercises
  41. 05: Linear Transformations
  42. 5.01: Linear Transformations
  43. 5.02: The Matrix of a Linear Transformation I
  44. 5.03: Properties of Linear Transformations
  45. 5.04: Special Linear Transformations in R
  46. 5.05: One-to-One and Onto Transformations
  47. 5.06: Isomorphisms
  48. 5.07: The Kernel and Image of A Linear Map
  49. 5.08: The Matrix of a Linear Transformation II
  50. 5.09: The General Solution of a Linear System
  51. 5.E: Exercises
  52. 06: Complex Numbers
  53. 6.01: Complex Numbers
  54. 6.02: Polar Form
  55. 6.03: Roots of Complex Numbers
  56. 6.04: The Quadratic Formula
  57. 6.E: Exercises
  58. 07: Spectral Theory
  59. 7.01: Eigenvalues and Eigenvectors of a Matrix
  60. 7.02: Diagonalization
  61. 7.03: Applications of Spectral Theory
  62. 7.04: Orthogonality
  63. 7.E: Exercises
  64. 08: Some Curvilinear Coordinate Systems
  65. 8.01: Polar Coordinates and Polar Graphs
  66. 8.02: Spherical and Cylindrical Coordinates
  67. 8.E: Exercises
  68. 09: Vector Spaces
  69. 9.01: Algebraic Considerations
  70. 9.02: Spanning Sets
  71. 9.03: Linear Independence
  72. 9.04: Subspaces and Basis
  73. 9.05: Sums and Intersections
  74. 9.06: Linear Transformations
  75. 9.07: Isomorphisms
  76. 9.08: The Kernel and Image of a Linear Map
  77. 9.09: The Matrix of a Linear Transformation
  78. 9.E: Exercises
  79. 10: Some Prerequisite Topics
  80. 10.01: Sets and Set Notation
  81. 10.02: Well Ordering and Induction
  82. 11: Introduction
  83. 11.01: Notes About These Notes
  84. 11.02: Introduction to Differential Equations
  85. 11.03: Classification of Differential Equations
  86. 11.04: First order ODEs
  87. 11.E: Introduction (Exercises)
  88. 12: First order ODEs
  89. 12.01: Integrals as solutions
  90. 12.02: Slope fields
  91. 12.03: Separable Equations
  92. 12.04: Linear equations and the integrating factor
  93. 12.05: Existence and Uniqueness of Solutions of Nonlinear Equations
  94. 12.5E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  95. 12.06: Substitution
  96. 12.07: Autonomous equations
  97. 12.08: Numerical methods- Eulers method
  98. 12.09: Exact Equations
  99. 12.10: First Order Linear PDE
  100. 12.E: First order ODEs (Exercises)
  101. 13: Applications of First Order Equations
  102. 13.01: Growth and Decay
  103. 13.1E: Growth and Decay (Exercises)
  104. 13.02: Cooling and Mixing
  105. 13.2E: Cooling and Mixing (Exercises)
  106. 13.03: Elementary Mechanics
  107. 13.3E: Elementary Mechanics (Exercises)
  108. 14: Higher order linear ODEs
  109. 14.01: Second order linear ODEs
  110. 14.02: The Method of Undetermined Coefficients I
  111. 14.2E: The Method of Undetermined Coefficients I (Exercises)
  112. 14.03: The Method of Undetermined Coefficients II
  113. 14.3E: The Method of Undetermined Coefficients II (Exercises)
  114. 14.04: Constant coefficient second order linear ODEs
  115. 14.05: Higher order linear ODEs
  116. 14.06: Reduction of Order
  117. 14.6E: Reduction of Order (Exercises)
  118. 14.07: Variation of Parameters
  119. 14.7E: Variation of Parameters (Exercises)
  120. 14.08: Mechanical Vibrations
  121. 14.09: Nonhomogeneous Equations
  122. 14.10: Forced Oscillations and Resonance
  123. 14.E: Higher order linear ODEs (Exercises)
  124. 15: Fourier series and PDEs
  125. 15.01: Boundary value problems
  126. 15.02: The Trigonometric Series
  127. 15.03: More on the Fourier Series
  128. 15.04: Sine and Cosine Series
  129. 15.05: Applications of Fourier Series
  130. 15.06: PDEs Separation of Variables and The Heat Equation
  131. 15.07: One Dimensional Wave Equation
  132. 15.08: DAlembert Solution of The Wave Equation
  133. 15.09: Steady State Temperature and the Laplacian
  134. 15.10: Dirichlet Problem in the Circle and the Poisson Kernel
  135. 15.E: Fourier Series and PDEs (Exercises)
  136. 16: Power series methods
  137. 16.01: Power Series
  138. 16.02: Series Solutions of Linear Second Order ODEs
  139. 16.03: Singular Points and the Method of Frobenius
  140. 16.E: Power series methods (Exercises)
  141. 17: Nonlinear Systems
  142. 17.01: Linearization Critical Points and Equilibria
  143. 17.02: Stability and Classication of Isolated Critical Points
  144. 17.03: Applications of Nonlinear Systems
  145. 17.04: Limit cycles
  146. 17.05: Chaos
  147. 17.06: Appendix B- Table of Laplace Transforms
  148. 17.E: Nonlinear Equations (Exercises)