Catalog

Differential Equations

Mathematics MIT CC BY-NC-SA 4.0 32 lectures

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Syllabus

  1. 1 Lecture 1: The Geometrical View of y'= f(x,y)
  2. 2 Lecture 2: Euler's Numerical Method for y'=f(x,y)
  3. 3 Lecture 3: Solving First-order Linear ODEs
  4. 4 Lecture 4: First-order Substitution Methods
  5. 5 Lecture 5: First-order Autonomous ODEs
  6. 6 Lecture 6: Complex Numbers and Complex Exponentials
  7. 7 Lecture 7: First-order Linear with Constant Coefficients
  8. 8 Lecture 8: Continuation
  9. 9 Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients
  10. 10 Lecture 10: Continuation: Complex Characteristic Roots
  11. 11 Lecture 11: Theory of General Second-order Linear Homogeneous ODEs
  12. 12 Lecture 12: Continuation: General Theory for Inhomogeneous ODEs
  13. 13 Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs
  14. 14 Lecture 14: Interpretation of the Exceptional Case: Resonance
  15. 15 Lecture 15: Introduction to Fourier Series
  16. 16 Lecture 16: Continuation: More General Periods
  17. 17 Lecture 17: Finding Particular Solutions via Fourier Series
  18. 18 Lecture 19: Introduction to the Laplace Transform
  19. 19 Lecture 20: Derivative Formulas
  20. 20 Lecture 21: Convolution Formula
  21. 21 Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs
  22. 22 Lecture 23: Use with Impulse Inputs
  23. 23 Lecture 24: Introduction to First-order Systems of ODEs
  24. 24 Lecture 25: Homogeneous Linear Systems with Constant Coefficients
  25. 25 Lecture 26: Continuation: Repeated Real Eigenvalues
  26. 26 Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
  27. 27 Lecture 28: Matrix Methods for Inhomogeneous Systems
  28. 28 Lecture 29: Matrix Exponentials
  29. 29 Lecture 30: Decoupling Linear Systems with Constant Coefficients
  30. 30 Lecture 31: Non-linear Autonomous Systems
  31. 31 Lecture 32: Limit Cycles
  32. 32 Lecture 33: Relation Between Non-linear Systems and First-order ODEs

Course materials