| WEEK |
DATE |
TOPICS |
| 1 |
1/22 |
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 |
1/29 |
Scalar Nonlinear Equs (Chap 5, secs 1, (2), 4 ?) |
| | |
- Existence and Uniqueness
- Sensitivity and Conditioning. backward error vs forward error
- Methods: Bisection, Newton, Secant.
- HW1 due Jan 29
|
| 3 |
2/05 |
... 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.
|
| 4 |
2/12 |
... Linear equations continued |
| | |
- Sensitivity and Conditioning.
- Methods: Gaussian Elimination and Back Substitution.
|
| 5 |
2/19 |
Nonlinear Equations -- Systems (Chap 5, secs 4-6) |
| | |
- Partial Derivatives: gradients, Jacobians.
- Fixed Point Methods. Newton's method.
- HW2 due Feb 19.
|
| 6 |
2/26 |
Polynomial Interpolation (Chap. 7, secs 1-3) |
| | |
- Existence and Uniqueness
- Methods: undetermined coefs.
|
| 6 |
2/28 |
MIDTERM I (on Thursday, in class). |
| | | |
| 7 |
3/05 |
... Interpolation continued |
| | |
- Methods: Lagrange polynomials. divided differences.
|
| ... | ... | Splines (Chap 7. sec 4) |
| | |
- Piecewise polynomial interpolation: splines.
- Two-dimensional interpolation/splines (from notes).
|
| 8 |
3/12 |
Linear Least Squares (Chap 3, secs 1, 2) |
| | |
- Existence and Uniqueness
- Normal equations. Projections.
- Orthogonal Transformations. Gram-Schmidt.
- HW3 due Mar 12.
|
| === |
3/18 |
Spring Break |
| | |
- Romp in the sand or the snow.
|
| 9 |
3/28 |
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.
|
| 10 |
4/02 |
... Uncontrained Optimization continued (methods) |
| | |
- One-dimension: Golden Section Search.
- Multi-dimensional methods: steepest descent, Newton, BFGS.
- Line Search
|
| 11 |
4/09 |
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.
- HW4 due Apr 09.
|
| 11 |
4/11 |
MIDTERM II (on Thursday, in class). |
| | | |
| 12 |
4/16 |
Numerical Integration and Quadrature (Chap 8, secs 1-4,7) |
| | |
- Existence and Uniqueness
- Numerical Quadrature (equally-spaced points).
- Adaptive Quadrature
- Richardson Extrapolation: Romberg.
|
| 13 |
4/23 |
Initial Val. Probs. for Ord. Diff. Equs |
| | |
- Existence and Uniqueness, stability of solutions
- Linear ODEs
- Methods: Euler, Backward Euler.
|
| 14 |
4/30 |
... ODEs continued |
| | |
- Accuracy and Stability: local vs global truncation error
- Runge-Kutta Methods
- HW5 due May 02.
|
-->
| 15 |
5/09 |
FINAL (on Thursday, 4-6pm). |
| | |
Date Confirmed
|
