| WEEK |
DATE |
TOPICS |
| 1 |
1/16 |
Scientific Computing - Goals and Fundamentals (Chap 1) |
| | |
- floating point arithmetic
- relative error
- conditioning vs stability: backward error vs forward error
- truncation error vs rounding error.
|
| 2 |
1/23 |
Scalar Nonlinear Equs (Chap 5, secs 1, (2), 4 ?) |
| | |
- Existence and Uniqueness
- Sensitivity and Conditioning. backward error vs forward error
- Methods: Bisection, Newton, Secant.
|
| 3 |
1/30 |
... Nonlinear equations continued |
| | |
- General Fixed Point Methods.
- Convergence Rates and Stopping Criteria
|
| ... | ... | Systems of Linear Equations (Chap 2, secs 1-4, up to 2.4.7) |
| | |
- Existence and Uniqueness
- Norms.
- HW1 due Jan 30
|
| 4 |
2/06 |
... Linear equations continued |
| | |
- Sensitivity and Conditioning.
- Methods: Gaussian Elimination and Back Substitution.
|
| 5 |
2/13 |
Nonlinear Equations -- Systems (Chap 5, secs 4-6) |
| | |
- Partial Derivatives: gradients, Jacobians.
- Fixed Point Methods. Newton's method.
|
| 6 |
2/20 |
Polynomial Interpolation (Chap. 7, secs 1-3) |
| | |
- Existence and Uniqueness
- Methods: undetermined coefs.
- HW2 due Feb 22.
|
| 7 |
2/27 |
... Interpolation continued |
| | |
- Methods: Lagrange polynomials. divided differences.
|
| ... | ... | Splines (Chap 7. sec 4) |
| | |
- Piecewise polynomial interpolation: splines.
- Two-dimensional interpolation/splines (from notes).
|
| 7 |
3/01 |
MIDTERM I (on Thursday, in class). |
| | | |
| 8 |
3/06 |
Linear Least Squares (Chap 3, secs 1, 2) |
| | |
- Existence and Uniqueness
- Normal equations. Projections.
- Orthogonal Transformations. Gram-Schmidt.
|
| === |
3/12 |
Spring Break |
| | |
- Romp in the sand or the snow.
|
| 9 |
3/20 |
Unconstrained Optimization Problems (Chap 6, esp. secs 1-5) |
| | |
- Existence and Uniqueness: coercive and convex functions
- Conditioning
- First & second order conditions for optimality, gradients, Hessians.
- HW3 due Mar 22.
|
| 10 |
3/27 |
... Uncontrained Optimization continued (methods) |
| | |
- One-dimension: Golden Section Search.
- Multi-dimensional methods: steepest descent, Newton, BFGS.
- Line Search
|
| 11 |
4/03 |
Constrained Optimization Problems (Chap 6, sec 7) |
| | |
- Equality constraints, inequality constraints
- First Order conditions for optimality: KKT conditions
- Penalty & barrier methods. (maybe dual ascent methods?)
- Linear Programs.
|
| 11 |
4/05 |
MIDTERM II (on Thursday, in class). |
| | | |
| 12 |
4/10 |
Numerical Integration and Quadrature (Chap 8, secs 1-4,7) |
| | |
- Existence and Uniqueness
- Numerical Quadrature (equally-spaced points).
- Adaptive Quadrature
- Richardson Extrapolation: Romberg.
|
| 13 |
4/17 |
Initial Val. Probs. for Ord. Diff. Equs |
| | |
- Existence and Uniqueness, stability of solutions
- Linear ODEs
- Methods: Euler, Backward Euler.
- HW4 due Apr 19.
|
| 14 |
4/24 |
... ODEs continued |
| | |
- Accuracy and Stability: local vs global truncation error
- Runge-Kutta Methods
|
| 15 |
5/01 |
Review.
|
| | |
- HW5 due May 01.
|
| 16 |
5/08 |
FINAL (on Tuesday, 4-6pm). |
| | |
Date Subject to Confirmation
|
