Differential Equations for Engineers

by Jiří Lebl

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A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.

Description from LibreTexts.

Publisher
Oklahoma State University
Subjects
Mathematics, Differential Equations
Licence
CC BY-SA 4.0, as LibreTexts states it
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. 0: Introduction
  7. 0.1: Notes About These Notes
  8. 0.2: Introduction to Differential Equations
  9. 0.3: Classification of Differential Equations
  10. 0.E: Introduction (Exercises)
  11. 1: First order ODEs
  12. 1.1: Integrals as solutions
  13. 1.2: Slope fields
  14. 1.3: Separable Equations
  15. 1.4: Linear equations and the integrating factor
  16. 1.5: Substitution
  17. 1.6: Autonomous equations
  18. 1.7: Numerical methods: Euler’s method
  19. 1.8: Exact Equations
  20. 1.9: First Order Linear PDE
  21. 1.E: First order ODEs (Exercises)
  22. 2: Higher order linear ODEs
  23. 2.1: Second order linear ODEs
  24. 2.2: Constant coefficient second order linear ODEs
  25. 2.3: Higher order linear ODEs
  26. 2.4: Mechanical Vibrations
  27. 2.5: Nonhomogeneous Equations
  28. 2.6: Forced Oscillations and Resonance
  29. 2.E: Higher order linear ODEs (Exercises)
  30. 3: Systems of ODEs
  31. 3.1: Introduction to Systems of ODEs
  32. 3.2: Matrices and linear systems
  33. 3.3: Linear systems of ODEs
  34. 3.4: Eigenvalue Method
  35. 3.5: Two dimensional systems and their vector fields
  36. 3.6: Second order systems and applications
  37. 3.7: Multiple Eigenvalues
  38. 3.8: Matrix exponentials
  39. 3.9: Nonhomogeneous systems
  40. 3.E: Systems of ODEs (Exercises)
  41. 4: Fourier series and PDEs
  42. 4.1: Boundary value problems
  43. 4.2: The Trigonometric Series
  44. 4.3: More on the Fourier Series
  45. 4.4: Sine and Cosine Series
  46. 4.5: Applications of Fourier Series
  47. 4.6: PDEs, Separation of Variables, and The Heat Equation
  48. 4.7: One Dimensional Wave Equation
  49. 4.8: D’Alembert Solution of The Wave Equation
  50. 4.9: Steady State Temperature and the Laplacian
  51. 4.10: Dirichlet Problem in the Circle and the Poisson Kernel
  52. 4.E: Fourier Series and PDEs (Exercises)
  53. 5: Eigenvalue problems
  54. 5.1: Sturm-Liouville problems
  55. 5.2: Application of Eigenfunction Series
  56. 5.3: Steady Periodic Solutions
  57. 5.E: Eigenvalue Problems (Exercises)
  58. 6: The Laplace Transform
  59. 6.1: The Laplace Transform
  60. 6.2: Transforms of derivatives and ODEs
  61. 6.3: Convolution
  62. 6.4: Dirac Delta and Impulse Response
  63. 6.5: Solving PDEs with the Laplace Transform
  64. 6.E: The Laplace Transform (Exercises)
  65. 7: Power series methods
  66. 7.1: Power Series
  67. 7.2: Series Solutions of Linear Second Order ODEs
  68. 7.3: Singular Points and the Method of Frobenius
  69. 7.E: Power series methods (Exercises)
  70. 8: Nonlinear Systems
  71. 8.1: Linearization, Critical Points, and Equilibria
  72. 8.2: Stability and Classification of Isolated Critical Points
  73. 8.3: Applications of Nonlinear Systems
  74. 8.4: Limit cycles
  75. 8.5: Chaos
  76. 8.E: Nonlinear Equations (Exercises)
  77. Appendix A: Linear Algebra
  78. A.1: Vectors, Mappings, and Matrices
  79. A.2: Matrix Algebra
  80. A.3: Elimination
  81. A.4: Subspaces, Dimension, and The Kernel
  82. A.5: Inner Product and Projections
  83. A.6: Determinant
  84. A.E: Linear Algebra (Exercises)
  85. Appendix B: Table of Laplace Transforms
  86. Back Matter
  87. Index
  88. Detailed Licensing
  89. Further Reading