# Scientific Computing

Warren Weaver Hall, room 101, Thursdays, 5:10 - 7 pm
Courant Institute of Mathematical Sciences
New York University
Spring Semester, 2012

## Lecture materials

Before even the first class, I recommend that you refresh your linear algebra, for example, using these notes by Jonathan Goodman.
Also get a CIMS computer account and start playing with MATLAB.

### 1. (Jan. 26th) Numerical Computing

Based on chapter 1 of textbook and chapter I in notes by Jonathan Goodman.
Here are some MATLAB scripts used as examples in the lecture notes: fibb.m, vect.m.

### 2. (Feb 2nd) Sources of Error

Based on chapter 1 of textbook and chapter I in notes by Jonathan Goodman.
Here are some MATLAB scripts used as examples in the lecture notes: harmonic.m (double precision) and harmonicSP.m (single precision). Also an example solution to the example homework problem: FirstDeriv.m and FirstDerivSP.m

### 3. (Feb 9th) Dense Linear Systems

Based on chapter 5 (Linear Systems) of textbook (sections 5.1-5.8).
Here is the MATLAB code for MyLU.m
For a more mathematical review of linear algebra consult these these notes by Jonathan Goodman, and for a more in-depth discussion consult these notes by Jonathan Goodman.

### 4. (Feb 16th) Symmetric, Overdetermined and Sparse Linear Systems

Based on chapter 5 (Linear Systems) of textbook.

### 5. (Feb 23rd) Eigen and Singular Values

Based on various sources, and marginally on chapter 6 (Eigenvalues and Eigenvectors) of the textbook.
Here are some MATLAB scripts used as examples in the lecture notes: Compression.m.

### 6. (Mar 1st) Solving Nonlinear Equations

Based on the first half of chapter 2 (Nonlinear equations) of the book.
Here are some MATLAB scripts used as examples in the lecture notes: FZero.m.

### 7. (Mar 8th) Optimization

Based on various sources, including these notes by Jonathan Goodman. The material on constrained optimization is advanced and optional.
Here are some MATLAB scripts used as examples in the lecture notes: Rosenbrock.m.

### 8. (Mar 22nd) Interpolation

See chapter 3 of textbook (Approximation of functions) and also these notes by Jonathan Goodman.
Here are some MATLAB scripts used as examples in the lecture notes: Runge1D.m, Hills2D.m, HillsIrreg2D.m.

### 9. (March 29th) Numerical Integration

See chapter 4 of textbook (Numerical differentiation and integration).

### 10. (April 5th and 12th) Monte Carlo

Based on these lecture notes by Jonathan Goodman. Further technical details on variance reduction are in these notes by Goodman.

### 11. (April 19th) ODEs

Based on chapter 7 (Ordinary Differential Equations) of the textbook and these lecture notes by Jonathan Goodman. A concise summary and two proofs of convergence of Euler's method not given in my lecture slides is in these notes by David Bindel.

### 12. (April 26th) PDEs

Based on various sources, just a brief sketch.