Below are summary handouts to lecture topics. These notes have been evolved over a few years. They are quite densely written and do not replace the book.

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 transformations	6. Lecture: Inverse transformation
Notes: Matrix product	7. Lecture: Image and kernel
8. Lecture: Basis	9. Lecture: Dimension
10. Lecture: Coordinates	13. Lecture: Orthogonal basis
14. Lecture: Gram-Schmidt	15. Lecture: Orthogonal matrices
16. Lecture: Linear fit	17. Lecture: Determinants I
18. Lecture: Determinants II	Notes: Eigenvalues
20. Lecture: Eigenvectors	21. Lecture: Diagnonalization
22. Lecture: Complex numbers	23. Lecture: Stability
24. Lecture: Symmetric matrices	25. Lecture: Differential equations I
26. Lecture: Differential equations II	27. Lecture: Nonlinear systems
28. Lecture: Function spaces and linear maps	29. Lecture: Differential equations III

Please send questions and comments to math21b@fas.harvard.edu

Math21b | Yum-Tong Siu | Fall 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University