| 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 |
1/27 |
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 Wed Jan 29
|
| 3 |
2/03 |
... 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 |
2/10 |
... Linear equations continued |
| | |
- Sensitivity and Conditioning.
- Methods: Gaussian Elimination and Back Substitution.
- HW2 due Mon Feb 10.
|
| 5 |
2/17 |
Nonlinear Equations -- Systems (Chap 5, secs 4-6) |
| | |
- Partial Derivatives: gradients, Jacobians.
- Fixed Point Methods. Newton's method.
|
| 6 |
2/24 |
MIDTERM I (on Monday, in class). |
| | | |
| 6 |
2/24 |
Polynomial Interpolation (Chap. 7, secs 1-3) |
| | |
- Existence and Uniqueness
- Methods: undetermined coefs.
|
| 7 |
3/02 |
... Interpolation continued |
| | |
- Methods: Lagrange polynomials. divided differences.
|
| ... | ... | Splines (Chap 7. sec 4) |
| | |
- Piecewise polynomial interpolation: splines.
- Two-dimensional interpolation/splines (from notes).
- HW3 due Mon Mar 02.
|
| === |
3/09 |
Spring Break |
| | |
- Romp in the sand or the snow.
|
| 8 |
3/16 |
Linear Least Squares (Chap 3, secs 1, 2) |
| | |
- Existence and Uniqueness
- Normal equations.
- Projections.
| ... | ... | Unconstrained Optimization Problems (Chap 6, esp. secs 1-5)
- Existence and Uniqueness: coercive and convex functions
- Conditioning
- First & second order conditions for optimality in 1D, gradients, Hessians.
- One-dimension: Golden Section Search.
|
| 9 |
3/23 |
... Unconstrained Optimization continued (multi-dimensional) |
| | |
- First & second order conditions for optimality (multi-dim): gradients, Hessians.
- Conditioning
- Multi-dimensional methods: steepest descent, Newton, BFGS.
- Line Search
- HW4 due Mon Mar 23.
|
| 10 |
3/30 |
Constrained Optimization Problems (Chap 6, sec 7) |
| | |
- Equality constraints, inequality constraints
- First Order conditions for optimality: KKT conditions
|
| 11 |
4/06 |
Enhanced Homework I (out Monday, due Tuesday). |
| | | |
| 11 |
4/06 |
Constrained Optimization Problems (Chap 6, sec 7) |
| | |
- Penalty & barrier methods. (maybe dual ascent methods?)
- Linear Programs.
|
| 12 |
4/13 |
Numerical Integration and Quadrature (Chap 8, secs 1-4,7) |
| | |
- Existence and Uniqueness
- Numerical Quadrature (equally-spaced points).
- Adaptive Quadrature
- Richardson Extrapolation: Romberg.
- HW5 due Wed Apr 15.
|
| 13 |
4/20 |
Initial Val. Probs. for Ord. Diff. Equs |
| | |
- Existence and Uniqueness, stability of solutions
- Linear ODEs
- Methods: Euler, Backward Euler.
|
| 14 |
4/27 |
... ODEs continued |
| | |
- Accuracy and Stability: local vs global truncation error
- Runge-Kutta Methods
- HW6 due Mon Apr 27.
|
| 15 |
5/04 |
Enhanced Homework II (out Monday, due Tuesday). |
| | | |
|
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