*Pre-lecture video:* Intro to Optimization (quiz)

- Optimization in one and $n$ dimensions

*Pre-lecture video:* Newton's method (quiz)

**Extra credit: Submit a practice exam final question!**

- Solving nonlinear equations in one and $n$ dimensions

*Pre-lecture video:* Rates and Orders of Convergence (quiz)

- Floating point: numbers in computers

*Pre-lecture video:* Finite Differences (quiz)

- Finite differences
- Floating point: numbers in computers

*Pre-lecture video:* Numerical differentiation (quiz)

- Fourier series
- Numerical Differentiation and Integration

*Pre-lecture video:* Fourier Analysis (quiz)

- Orthogonal polynomials
- Fourier series

*Reading:*

- Klein, Chapter 10
- Kutz, Chapter 4

*Pre-lecture video:* Interpolation error (quiz)

- Function spaces and interpolation
- Order of convergence

*Reading:*

- Klein, Chapter 10
- Kutz, Chapter 4 (and 3 for review)

*Pre-lecture video:* Interpolation (quiz)

- Computing the SVD
- Applications of eigenvalues
- Function spaces and interpolation

*Reading:*

- Klein, Chapter 10
- Kutz, Chapter 4 (and 3 for review)

*Pre-lecture video:* Inverse iteration (quiz)

- Inverse iteration
- Orthogonal iteration

*Reading:*

- Klein, Chapter 12
- Kutz, Section 2.4

*Pre-lecture video:* Power iteration (quiz)

**Extra credit: Submit a practice exam question!**

- Eigenvalues and Eigenvectors
- Power iteration and its variants
- Schur form

*Reading:*

- Klein, Chapter 12
- Kutz, Section 2.4

*Pre-lecture video:* Eigenvalues (quiz)

- Applications of the SVD
- Principal component analysis
- Low-rank approximation

*Reading:*

- Klein, Chapter 12
- Kutz, Section 2.4

*Pre-lecture/review video:* Singular Value Decomposition (part 2) (quiz)

- Singular Value Decomposition

*Reading:*

- Klein, Chapter 11
- Kutz, Chapter 15

*Pre-lecture/review video:* Singular Value Decomposition (quiz)

- Applications of Least Squares: Machine Learning

*Reading:*

- Klein, Chapter 9 and 11,

*Pre-lecture/review video:* Least squares and data fitting (quiz)

- Data fitting/linear regression

*In-class quiz:* Least squares

*Reading:* Klein, Chapters 9 and 11

*Pre-lecture/review video:* Gram-Schmidt process (quiz)

- Gram-Schmidt and Modified Gram-Schmidt
- QR factorization
- Least Squares problems

*Reading:* Klein, Chapter 9

*Pre-lecture/review video:* Inner products (quiz)

- Orthogonality and QR

*Reading:* Klein, Chapter 9

*Review video:* Point-normal form

*Pre-lecture/review video:* Finding nullspaces of matrices (quiz)

- Nullspace finding
- Computing flows and circuits

*In-class quiz:* Applications of Gaussian Elimination II

*Reading:* Klein, Chapter 8

*Pre-lecture material:* Errors and condition numbers (quiz)

- LU factorization: applications, errors, condition number
- Inner product

*In-class quiz:* Applications of Gaussian Elimination

*Reading:* Klein, Chapter 8

*Pre-lecture material:* Rank and Nullspace (quiz)

- Properties of linear functions
- Accuracy and Pivoting
- Cost of LU factorization

*In-class quiz:* Gaussian Elimination

*Reading:* Klein, Chapter 6

*Pre-lecture material:* Norms (quiz)

- Linear systems
- Gaussian elimination
- LU factorization

*Review video:* LU factorization (instead of reading)

*Reading:* Klein, Chapter 7

*Pre-lecture material:* Linear Independence (quiz)

- Bases and Linear Dependence
- Dimension and Rank

*In-class quiz:* Linear indepence

*Reading:* Klein, Chapters 5

*Pre-lecture material:* Ins and outs of matrices (quiz)

- Matrix-matrix product
- Applications of Matrices
- Back-substitution (intro)

*Class recording:* video

*Reading:* Klein, Chapter 4

*Pre-lecture material:* Matrix multiplication (quiz) (code q)

- Linear functions
- Representation by Matrices
- Matrix-vector product

*Reading:* Klein, Chapters 3/4

*Pre-lecture material:* Matrices (quiz)

- Quiz review
- Convex combinations
- einsum

*In-class quiz:* Combinations

*Review video:* Convex combinations and einsum

*Reading:* Klein, Chapters 1 and 2

*Pre-lecture material:* Combinations (quiz)

- Vectors, combinations, coordinates

*Reading:* Klein, Chapters 1 and 2

*Pre-lecture material:* Vectors and vector spaces (quiz)

*Pre-lecture material:* Grading policies intro (quiz)

- Discussion of Linear Algebra Pre-Quiz

*Review video:* Numpy intro

*Reading:* Python and Numpy references

*Pre-lecture material:* Linear algebra pre-quiz (not for credit)

- What is Scientific Computing?
- Python intro