21 B
Mathematics Math21b Spring 2007
Linear Algebra and Differential Equations
Course Head: Oliver Knill
Office: SciCtr 434

Corrected typos in the Fourier/PDE handout:
  • In the definition of even function on the first page, there had been a sign missing. Even means f(x)=f(-x).
  • In the EXAMPLE block after PARSEVAL, the coefficient bk had been called ak before.
  • In the block SOLVING THE WAVE EQUATION WITH RFOURIER THEORY, there had been an "n" missing in cos(n c t)
Below are summary handouts to lecture topics. These notes have been evolved since a few years. They are quite densely written and do not replace the book of course. If you find typos, please email them or talk to me about it. Errata found after the notes being distributed are acknowledged to the right. The files found here are already corrected. Book errata

1. Lecture: solving linear equations. 2. Lecture: Gauss-Jordan elemination.
3. Lecture: On systems of linear equations 4. Lecture: Linear transformations
5. Lecture: Geometry of linear trafos 6. Lecture: Inverse transformation
7. Lecture: Matrix product 8. Lecture: Image and kernel
9. Lecture: Basis 10. Lecture Dimension
11. Lecture: Coordinates 12. Lecture: Functionspace
14. Lecture: Orthogonal basis 15. Lecture: Gram-Schmid
16. Lecture: Orthogonal matrices 17. Lecture: Linear fit
18. Lecture: Determinant I 19. Lecture: Determinant II
20. Lecture: Discrete dynamical systems 21. Lecture: Eigenvalues
22. Lecture: Eigenvectors 23. Lecture: Diagonalization
24. Lecture: Complex numbers 25. Lecture: Stability
26. Lecture: Symmetric Matrices 27. Lecture: Differential equations I
28. Lecture: Differential equations II 29. Lecture: Nonlinear systems
30. Lecture: Linear maps 31. Lecture: Differential equations
Please send questions and comments to
Math21b | Oliver Knill | Spring 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University