M A T H 2 1 B
Mathematics Math21b Spring 2007
Linear Algebra and Differential Equations
Supplements
Course Head: Oliver Knill
Office: SciCtr 434

 Section 9.4, nonlinear dynamics, the missing chapter, written by Otto Bretscher. We also have a HTML version of the handout. Handout for last week with homework. There are 2 HW assignments next week. One about Fourier theory, an other about partial differential equations. Both homework assignements are on the handout. [HTML version], [PDF]. 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@fas.harvard.edu
Math21b | Oliver Knill | Spring 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University