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

• A sheet with some logistics.
• All the summaries on the worksheets are collected 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.