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Differential Equations and Linear Algebra

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Differential Equations and Linear Algebra

In this book, you will learn key techniques for solving differential equations that arise in science and engineering applications. You will also build a strong foundation in linear algebra concepts that support these methods.

Mathematics
Author
Anup Lamichhane
Publisher
Oho Northern University
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 97 sections
  1. 01: First order ODEs
  2. 1.01: Introduction
  3. 1.02: Integrals as solutions
  4. 1.03: Slope fields
  5. 1.04: Separable Equations
  6. 1.05: Linear equations and the integrating factor
  7. 1.06: Substitution
  8. 1.07: Exact Equations
  9. 1.08: Autonomous equations
  10. 1.09: Existence and Uniqueness of Solutions of Nonlinear Equations
  11. 1.9E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
  12. 1.10: Numerical methods- Eulers method
  13. 1.11: First Order Linear PDE
  14. 1.E: First order ODEs (Exercises)
  15. 02: Applications of First Order Equations
  16. 2.01: Growth and Decay
  17. 2.1E: Growth and Decay (Exercises)
  18. 2.02: Cooling and Mixing
  19. 2.2E: Cooling and Mixing (Exercises)
  20. 2.03: Elementary Mechanics
  21. 2.3E: Elementary Mechanics (Exercises)
  22. 2.04: Autonomous Second Order Equations
  23. 2.4E: Autonomous Second Order Equations (Exercises)
  24. 2.05: Applications to Curves
  25. 2.5E: Applications to Curves (Exercises)
  26. 03: Systems of Equations
  27. 3.01: Systems of Equations Geometry
  28. 3.02: Systems of Equations Algebraic Procedures
  29. 3.03: Gaussian Elimination
  30. 3.04: Uniqueness of the Reduced Row-Echelon Form
  31. 3.05: Applications of system of linear equations
  32. 3.06: Dimensionless Variables
  33. 3.07: Exercises
  34. 04: Matrices and Determinants
  35. 4.01: Matrix Arithmetic
  36. 4.02: The Transpose
  37. 4.03: The Identity and Inverses
  38. 4.04: Elementary Matrices
  39. 4.05: More on Matrix Inverses
  40. 4.06: LU
  41. 4.07: Determinants
  42. 4.08: Applications of the Determinant
  43. 4.09: Eigenvalues and Eigenvectors of a Matrix
  44. 4.10: Diagonalization
  45. 4.11: Determinant Exercises
  46. 4.E: Exercises
  47. 05: R
  48. 5.01: Vectors in R
  49. 5.02: Vector Algebra
  50. 5.03: Geometric Meaning of Vector Addition
  51. 5.04: Length of a Vector
  52. 5.05: Geometric Meaning of Scalar Multiplication
  53. 5.06: Spanning Linear Independence and Basis in R
  54. 5.07: Rank and Homogeneous Systems
  55. 5.E: Exercises
  56. 06: Higher order linear ODEs
  57. 6.01: Homogeneous Linear Equations
  58. 6.1.01: Homogeneous Linear Equations (Exercises)
  59. 6.02: Second order linear ODEs
  60. 6.03: Constant coefficient second order linear ODEs
  61. 6.04: Introduction to Linear Higher Order Equations
  62. 6.4.01: Higher order linear ODEs
  63. 6.4E: Introduction to Linear Higher Order Equations (Exercises)
  64. 6.05: Nonhomogeneous Linear Equations
  65. 6.5.01: Nonhomgeneous Linear Equations (Exercises)
  66. 6.06: The Method of Undetermined Coefficients I
  67. 6.6.01: The Method of Undetermined Coefficients I (Exercises)
  68. 6.07: The Method of Undetermined Coefficients II
  69. 6.7E: The Method of Undetermined Coefficients II (Exercises)
  70. 6.08: Reduction of Order
  71. 6.8E: Reduction of Order (Exercises)
  72. 6.09: Variation of Parameters
  73. 6.9E: Variation of Parameters (Exercises)
  74. 6.10: Mechanical Vibrations
  75. 6.11: Nonhomogeneous Equations
  76. 6.12: Forced Oscillations and Resonance
  77. 6.E: Higher order linear ODEs (Exercises)
  78. 07: The Laplace Transform
  79. 7.01: Introduction to the Laplace Transform
  80. 7.1E: Introduction to the Laplace Transform (Exercises)
  81. 7.02: The Inverse Laplace Transform
  82. 7.2E: The Inverse Laplace Transform (Exercises)
  83. 7.03: The Laplace Transform
  84. 7.04: Solution of Initial Value Problems
  85. 7.4E: Solution of Initial Value Problems (Exercises)
  86. 7.05: Transforms of derivatives and ODEs
  87. 7.06: Convolution
  88. 7.07: The Unit Step Function
  89. 7.7E: The Unit Step Function (Exercises)
  90. 7.08: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
  91. 7.8.01: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
  92. 7.09: Dirac Delta and Impulse Response
  93. 7.10: Constant Coefficient Equations with Impulses
  94. 7.10.01: Constant Coefficient Equations with Impulses (Exercises)
  95. 7.11: Solving PDEs with the Laplace Transform
  96. 7.12: A Brief Table of Laplace Transforms
  97. 7.E: The Laplace Transform (Exercises)