This is the website of my Spring 2018 Math 21b section. The course website can be found here.

## Worksheets

Below appear the worksheets and further material.

- 1/26, Lecture 1: introduction and linear equations.
- 1/29, Lecture 2: Gauss-Jordan elimination.
- 1/31, Lecture 3: the number of solutions.
- 2/2, Lecture 4: linear transformations.
- 2/5, Lecture 5: linear transformations in geometry.
- 2/7, Lecture 6: matrix algebra.
- 2/9, Lecture 7: images and kernels.
- 2/12, Lecture 8: bases.
- 2/14, Lecture 9: dimension.
- 2/16, Lecture 10: coordinates.
- 2/21, Lecture 11: linear spaces.
- 2/23, Lecture 12: orthogonality.
- 2/26, Midterm 1 review: question sheet.
- 2/28, Lecture 13: Gram-Schmidt and QR-decompositions.
- 3/2, Lecture 14: orthogonal transformations.
- 3/6, Lecture 15: least squares and data fitting.
- 3/8, Lecture 16: determinants I.
- 3/10, Lecture 17: determinants II.
- 3/19, Lecture 18: eigenvalues, eigenvectors, and discrete dynamical systems.
- 3/21, Lecture 19: eigenspaces.
- 3/23, Lecture 20: similarity and diagonalization.
- 3/26, Lecture 21: complex eigenvalues and some notes on circulant matrices.
- 3/28, Lecture 22: asymptotic stability.
- 3/30, Lecture 23: symmetric matrices and the spectral theorem.
- 4/2, Midterm 2 review: question sheet.
- 4/4, Lecture 24: differential equations I.
- 4/6, Lecture 25: differential equations II.
- 4/9, Lecture 26: non-linear systems.
- 4/11, Lecture 27: differential operators.
- 4/13, Lecture 28: the ODE cookbook.
- 4/16, Lecture 29: Fourier series I.
- 4/18, Lecture 30: Fourier series II.
- 4/20, Lecture 31: Partial differential equations I.
- 4/23, Lecture 32: Partial differential equations II.
- 4/25, Final review: question sheet.