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Course18.0332 lectures25 h 26 min

Differential Equations

Prof. Haynes Miller and Prof. Arthur Mattuck · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: The Geometrical View of y'= f(x,y) 49 min · Video
  2. Lecture 2: Euler's Numerical Method for y'=f(x,y) 51 min · Video
  3. Lecture 3: Solving First-order Linear ODEs 51 min · Video
  4. Lecture 4: First-order Substitution Methods 51 min · Video
  5. Lecture 5: First-order Autonomous ODEs 46 min · Video
  6. Lecture 6: Complex Numbers and Complex Exponentials 46 min · Video
  7. Lecture 7: First-order Linear with Constant Coefficients 42 min · Video
  8. Lecture 8: Continuation 51 min · Video
  9. Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients 50 min · Video
  10. Lecture 10: Continuation: Complex Characteristic Roots 47 min · Video
  11. Lecture 11: Theory of General Second-order Linear Homogeneous ODEs 51 min · Video
  12. Lecture 12: Continuation: General Theory for Inhomogeneous ODEs 47 min · Video
  13. Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs 48 min · Video
  14. Lecture 14: Interpretation of the Exceptional Case: Resonance 45 min · Video
  15. Lecture 15: Introduction to Fourier Series 50 min · Video
  16. Lecture 16: Continuation: More General Periods 50 min · Video
  17. Lecture 17: Finding Particular Solutions via Fourier Series 46 min · Video
  18. Lecture 19: Introduction to the Laplace Transform 48 min · Video
  19. Lecture 20: Derivative Formulas 52 min · Video
  20. Lecture 21: Convolution Formula 45 min · Video
  21. Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs 45 min · Video
  22. Lecture 23: Use with Impulse Inputs 45 min · Video
  23. Lecture 24: Introduction to First-order Systems of ODEs 48 min · Video
  24. Lecture 25: Homogeneous Linear Systems with Constant Coefficients 50 min · Video
  25. Lecture 26: Continuation: Repeated Real Eigenvalues 47 min · Video
  26. Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients 51 min · Video
  27. Lecture 28: Matrix Methods for Inhomogeneous Systems 47 min · Video
  28. Lecture 29: Matrix Exponentials 49 min · Video
  29. Lecture 30: Decoupling Linear Systems with Constant Coefficients 48 min · Video
  30. Lecture 31: Non-linear Autonomous Systems 48 min · Video
  31. Lecture 32: Limit Cycles 46 min · Video
  32. Lecture 33: Relation Between Non-linear Systems and First-order ODEs 51 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Taught by
Prof. Haynes Miller, Prof. Arthur Mattuck
Term
Spring 2010
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Haynes Miller, Prof. Arthur Mattuck. Differential Equations. Spring 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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