Lectures (Video)
- 1. The Geometrical View
- 2. Euler's Numerical Method
- 3. Solving First-order Linear ODE's
- 4. First-order Substitution Methods
- 5. First-order Autonomous ODE's
- 6. Complex Numbers
- 7. First-order Linear ODEs with Constant Coefficients
- 8. Applications of First-order Linear ODEs with Constant Coefficients
- 9. Solving Second-order Linear ODE's with Constant Coefficients
- 10. Complex Characteristic Roots
- 11. Theory of General Second-order Linear Homogeneous ODE's
- 12. Stability Criteria
- 13. Particular Solution to Inhomogeneous ODE's
- 14. Resonance
- 15. Introduction to Fourier Series
- 16. More General Periods
- 17. Finding Particular Solutions via Fourier Series
- 19. Introduction to the Laplace Transform
- 20. Derivative Formulas
- 21. Convolution Formula
- 22. Using Laplace Transform to Solve ODEs
- 23. Impulse Inputs
- 24. First-order Systems of ODEs
- 25. Homogeneous Linear Systems
- 26. Repeated Real Eigenvalues
- 27. Sketching Solutions of Homogeneous Linear System
- 28. Matrix Methods for Inhomogeneous Systems
- 29. Matrix Exponentials
- 30. Decoupling Linear Systems
- 31. Non-linear Autonomous Systems
- 32. Limit Cycles
- 33. Relation Between Non-linear Systems and First-order ODEs
Differential Equations - Lecture 15
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Lecture 15 - Introduction to Fourier Series
Introduction to Fourier Series; Basic Formulas for Period 2(pi).
Prof. Arthur Mattuck, Prof. Haynes Miller
18.03 Differential Equations, Spring 2006 (Massachusetts Institute of Technology: MIT OpenCourseWare) http://ocw.mit.edu Date accessed: 2008-12-23 License: Creative Commons BY-NC-SA |
