| WEEK |
DATE |
TOPICS |
| 1 |
1/18 |
Scientific Computing - Goals and Fundamentals (H: Chap 1. A&G: 1.1-1.2, 2.1-2.3) |
| | |
- floating point arithmetic
- relative error
- conditioning vs stability: backward error vs forward error
- truncation error vs rounding error.
|
| 2 |
1/23 |
Scalar Nonlinear Equs (H: 5.1 (5.2), 5.4. A&G: 3.1-3.4 ) |
| | |
- Existence and Uniqueness
- Sensitivity and Conditioning. backward error vs forward error
- Methods: Bisection, Newton, Secant.
- HW1 due Wed Jan 25
|
| 3 |
1/30 |
... Nonlinear equations continued |
| | |
- General Fixed Point Methods.
- Convergence Rates and Stopping Criteria
|
| ... | ... | Systems of Linear Equations (H: 2.1-2.4.7. A&G: Chap 9, 9.1) |
| | |
- Existence and Uniqueness
- Norms.
|
| 4 |
2/06 |
... Linear equations continued |
| | |
- HW2 due Mon Feb 06.
- Sensitivity and Conditioning.
- Methods: Gaussian Elimination and Back Substitution.
|
| 5 |
2/13 |
Nonlinear Equations -- Systems (H: 5.4-5.6, [A&G: Chap 9]) |
| | |
- Partial Derivatives: gradients, Jacobians.
- Fixed Point Methods. Newton's method.
|
| 5 |
2/13 |
Enhanced Homework I (due Monday). |
| | | |
| 6 |
2/20 |
Polynomial Interpolation (H: 7.1-7.3. A&G: 7.1-7.3) |
| | |
- Existence and Uniqueness
- Methods: undetermined coefs.
- Methods: Lagrange polynomials. divided differences.
|
| 7 |
2/27 |
Splines (H: 7.4. A&G: 11.3, 11.6) |
| | |
- HW3 due Mon Feb 27.
- Piecewise polynomial interpolation: splines.
- Two-dimensional interpolation/splines (from notes).
|
| === |
3/06 |
SPRING BREAK |
| | |
- Romp in the virtual sand.
|
| 8 |
3/13 |
Linear Least Squares (H: 3.1-3.2. A&G: 6.1) |
| | |
- Existence and Uniqueness
- Normal equations.
- Projections.
|
| 9 |
3/20 |
Unconstrained Optimization Problems (H: 6.1-6.5. A&G: Chap 9, 3.5,9.2-9.3) |
| | |
- Existence and Uniqueness: coercive and convex functions
- Conditioning
- First & second order conditions for optimality in 1D, gradients, Hessians.
- One-dimension: Golden Section Search.
|
| | |
- HW4 due Mon Mar 20.
- Line Search
|
| 10 |
3/22 |
Enhanced Homework II (due Wednesday). |
| | | |
| 10 |
3/27 |
... Unconstrained Optimization continued (multi-dimensional) |
| | |
- First & second order conditions for optimality (multi-dim): gradients, Hessians.
- Conditioning
- Multi-dimensional methods: steepest descent, Newton, BFGS.
|
| 11 |
4/03 |
Constrained Optimization Problems (H: 6.7. A&G: 9.3) |
| | |
- Equality constraints, inequality constraints
- First Order conditions for optimality: KKT conditions
- (Penalty & barrier methods.)
- Linear Programs.
|
| 12 |
4/10 |
Numerical Integration and Quadrature (H: 8.1-8.4, 8.7. A&G: 15.1-15.2,15.4-15.5) |
| | |
- Existence and Uniqueness
- Numerical Quadrature (equally-spaced points).
- Adaptive Quadrature
- Richardson Extrapolation: Romberg.
|
| 13 |
4/17 |
Initial Val. Probs. for Ord. Diff. Equs (H: 9.1-9.3. A&G: 16.1-16.6. |
| | |
- HW5 due Mon Apr 17.
- Existence and Uniqueness, stability of solutions
- Linear ODEs
- Methods: Euler, Backward Euler.
|
| 14 |
4/24 |
... ODEs continued |
| | |
- Accuracy and Stability: local vs global truncation error
- Runge-Kutta Methods
Review |
| 15 |
4/24 |
Last day of class |
| XX |
5/01 |
Enhanced Homework III (due Monday). |
| | | |
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