Starts at 3:00pm *sharp* in 4403 Siebel.

To take a conflict final, you must request permission by email to Andreas or Eric. Just showing up or having filled out the Doodle poll is not enough. When emailing, please provide the reason why you are requesting to take the conflict exam.

Starts at 9:00am *sharp* in the Education Building, room 2.

Note that our official time slot starts at 8am, but since the exam is only 90 minutes long, we'll start a little later.

To take a conflict final, you must request permission by email to Andreas or Eric. Just showing up or having filled out the Doodle poll is not enough. When emailing, please provide the reason why you are requesting to take the conflict exam.

Starts at 8:00am *sharp*. Please be on time.

The exam will take place in Lincoln Hall Theater for both sections together.

*Pre-lecture material:* Floating Point (Quiz)

*In-class work:* Floating Point

- Constrained Optimization in practice
- Floating Point arithmetic

*Readings:*

*Pre-lecture material:* Constrained Optimization (Quiz)

*In-class work:* Optimization

- Golden Section Search
- Steepest Descent
- Newton's method in $n$ dimensions

*Readings:*

*Pre-lecture material:* Optimization (Quiz)

*In-class work:* Nonlinear equations

- Nonlinear equations in practice
- Intro to Optimization

*Readings:*

*Pre-lecture material:* (no video) (Review Quiz) (for credit)

- Solving nonlinear equations
- Bisection Method
- Convergence order

*Readings:*

*Pre-lecture material:* Newton's method (Quiz)

*In-class work:* Numerical Integration

- Finite Differences
- Calculus with interpolants: Integration

*Readings:*

*Pre-lecture material:* Rate and Order of Convergence (Quiz)

*In-class work:* Numerical Differentiation

- Fourier Interpolation
- Calculus with interpolants: Differentiation

*Readings:*

Starts at 6:30pm *sharp*. Please be on time.

- If you are in Section M, please go to 1320 DCL.
- If you are in Section N, please go to 1404 Siebel.

*Pre-lecture material:* Interpolation Error (Quiz)

*In-class work:* Interpolation: Error and Piecewise

- Interpolation Error
- Interpolation Node Choice
- Piecewise Polynomial Interpolation

*Readings:*

*Pre-lecture material:* Interpolation (Quiz)

*In-class work:* Interpolation

- Principal Component Analysis
- Least Squares Problems using the SVD
- Interpolation

*Readings:*

- Notes Section 10
- Klein, Section 10.4

*Pre-lecture material:* Least Squares using the SVD (Quiz)

*In-class work:* SVD Applications

- Applications of the SVD
- Low-rank approximation
- Principal Component Analysis
- Least Squares Problems

*Readings:*

- Notes Section 9
- Klein, Chapter 11

(no pre-lecture for today)

- Markov chains
- Singular Value Decomposition (SVD)

*In-class work:* SVD

*Readings:*

- Notes Section 8
- Klein, Chapter 11

*Pre-lecture material:* SVD (Quiz)

- Power iteration and its variants (inverse iteration, Rayleigh quotient iteration)
- Orthogonal Iteration

*Readings:*

- Notes Section 8
- Klein, Chapter 11

*Pre-lecture material:* Power iteration (Quiz)

- Eigenvalue transformations
- Rayleigh quotient
- Power iteration and its variants (inverse iteration, Rayleigh quotient iteration)

*In-class work:* Eigenvalues

*Readings:*

- Notes Section 7
- Klein, Chapter 12

*Pre-lecture material:* Eigenvalues (Quiz)

- Least squares using QR
- Data fitting

*In-class work:* Least squares

*Readings:*

- Notes Section 6
- Notes Section 7
- Klein, Chapter 12

*Pre-lecture material:* QR factorization (Quiz

- QR factorization: Construction, properties
- Applications of QR

*In-class work:* QR (Discussion)

*Readings:*

- Notes Section 5
- Notes Section 6
- Klein, Chapters 8/9

*Pre-lecture material:* Gram-Schmidt process, original and 'modified' (Quiz)

- Projections
- Gram-Schmidt ('original' and 'modified')

*In-class work:* Projection

*Readings:*

- Notes Section 5
- Klein, Chapters 8/9

Starts at 6:30pm *sharp*. Please be on time.

- If you are in Section M, please go to 1320 DCL.
- If you are in Section N, please go to 1404 Siebel.

*Pre-lecture material:* Orthogonalization (Quiz)

- Orthogonal vectors
- Point-normal form
- Orthogonal matrices

*In-class work:* Gram-Schmidt

*Readings:*

- Notes Section 5
- Klein, Chapters 8/9

*Pre-lecture material:* Inner Products (Quiz)

- Applications of LU
- Orthogonality

*In-class work:* LU Applications

*Readings:*

- Notes Section 4
- Klein, Chapters 8/9

*Pre-lecture material:* Finding Nullspaces (Quiz)
(**UPDATED** Feb 22)

- Pivoted LU review, non-square LU

*In-class work:* Pivoting

*Readings:*

- Notes Section 3
- Klein, Chapters 7

*Pre-lecture material:* Computational Cost and Big-O Notation (Quiz)

- LU factorization
- Pivoting

*In-class work:* LU (part 2)

*Readings:*

- Notes Section 3
- Klein, Chapter 7

*Pre-lecture material:* LU (Quiz)

- Forward/Backward Substitution
- Elimination Matrices
- LU factorization

*In-class work:* LU

*Readings:*

- Notes Section 3
- Klein, Chapter 7

*Pre-lecture material:* Elimination matrices (Quiz)

- Matrix Norms
- Condition number

*In-class work:* Matrix norms

*Readings:*

*Pre-lecture material:* Matrix Norms (Quiz)

- Vector Norms
- Relative/absolute error

*In-class work:* Norms

*Readings:*

See Lecture 5 for Section M.

*Pre-lecture material:* Norms (Quiz)

- Computational Linear Algebra

*In-class work:* Computational Linear Algebra

*Readings:*

- Klein textbook, chapters 1-5 contain what you should
*already*know about linear algebra

See Lecture 4 for Section M.

See Lecture 3 for Section M.

See Lecture 2 for Section M.

- What is Scientific Computing?
- Python intro

*In-class work:* Complexity of linear system solve

*Readings:*

- Klein textbook, chapters 1-5 contain what you should
*already*know about linear algebra - Scipy lectures, Section 1.2

See Lecture 1 for Section M.