Learn · Differential Equations

Lecture 3 of 32Video Lectures51 min

Lecture 3: Solving First-order Linear ODEs

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

At MIT OpenCourseWare Transcript

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From
Differential Equations, Massachusetts Institute of Technology (at MIT OpenCourseWare)
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
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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All the 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