Notes on Diffy Qs

Supported by the National Science Foundation.

About this Course

This course is designed to be a companion to Notes on Diffy Qs: Differential Equations for Engineers and was prepared by the book's author, Jiri LeblThe problem sets contain over 400 interactive, algorithmic problems and map directly to textbook sections.

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Problem Sets

  1. Edfinity Demo
  2. Sec 0.2: Introduction to differential equations
  3. Sec 0.3: Classification of differential equations
  4. Sec 1.1: Integrals as solutions
  5. Sec 1.2: Slope fields
  6. Sec 1.3: Separable equations
  7. Sec 1.4: Linear equations and the integrating factor
  8. Sec 1.5: Substitution
  9. Sec 1.6: Autonomous equations
  10. Sec 1.7: Numerical methods: Euler’s method
  11. Sec 1.8: Exact equations
  12. Sec 2.1: Second order linear ODEs
  13. Sec 2.2: Constant coefficient second order linear ODEs
  14. Sec 2.3: Higher order linear ODEs
  15. Sec 2.4: Mechanical vibrations
  16. Sec 2.5: Nonhomogeneous equations
  17. Sec 2.6: Forced oscillations and resonance
  18. Sec 3.1: Introduction to systems of ODEs
  19. Sec 3.2: Matrices and linear systems
  20. Sec 3.3: Linear systems of ODEs
  21. Sec 3.4: Eigenvalue method
  22. Sec 3.5: Two dimensional systems and their vector fields
  23. Sec 3.6: Second order systems and applications
  24. Sec 3.7: Multiple eigenvalues
  25. Sec 3.8: Matrix exponentials
  26. Sec 3.9: Nonhomogeneous systems
  27. Sec 4.1: Boundary value problems
  28. Sec 4.2: The trigonometric series
  29. Sec 4.3: More on the Fourier series
  30. Sec 4.4: Sine and cosine series
  31. Sec 4.5: Applications of Fourier series
  32. Sec 4.6: PDEs, separation of variables, and the heat equation
  33. Sec 4.7: One dimensional wave equation
  34. Sec 4.8: D’Alembert solution of the wave equation
  35. Sec 4.9: Steady state temperature and the Laplacian
  36. Sec 4.10: Dirichlet problem in the circle and the Poisson kernel
  37. Sec 5.1: Sturm-Liouville problems
  38. Sec 6.1: The Laplace transform
  39. Sec 6.2: Transforms of derivatives and ODEs
  40. Sec 6.3: Convolution
  41. Sec 6.4: Dirac delta and impulse response
  42. Sec 7.1: Power series
  43. Sec 7.2: Series solutions of linear second order ODEs
  44. Sec 7.3: Singular points and the method of Frobenius
  45. Sec 8.1: Linearization, critical points, and equilibria
  46. Sec 8.2: Stability and classification of isolated critical points
  47. Sec 8.3: Applications of nonlinear systems
  48. Sec 8.4: Limit cycles

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Contributors

Jiri Lebl
Oklahoma State University

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