WEEK 
DATE 
TOPICS 
1 
1/18 
Scientific Computing  Goals and Fundamentals (H: Chap 1. A&G: 1.11.2, 2.12.3) 
 
 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: 3.13.4 ) 
 
 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: 2.12.4.7. 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: 5.45.6, [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: 7.17.3. A&G: 7.17.3) 
 
 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.
 Twodimensional interpolation/splines (from notes).

=== 
3/06 
SPRING BREAK 
 
 Romp in the virtual sand.

8 
3/13 
Linear Least Squares (H: 3.13.2. A&G: 6.1) 
 
 Existence and Uniqueness
 Normal equations.
 Projections.

9 
3/20 
Unconstrained Optimization Problems (H: 6.16.5. A&G: Chap 9, 3.5,9.29.3) 
 
 Existence and Uniqueness: coercive and convex functions
 Conditioning
 First & second order conditions for optimality in 1D, gradients, Hessians.
 Onedimension: Golden Section Search.

 
 HW4 due Mon Mar 20.
 Line Search

10 
3/22 
Enhanced Homework II (due Wednesday). 
  
10 
3/27 
... Unconstrained Optimization continued (multidimensional) 
 
 First & second order conditions for optimality (multidim): gradients, Hessians.
 Conditioning
 Multidimensional 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: 8.18.4, 8.7. A&G: 15.115.2,15.415.5) 
 
 Existence and Uniqueness
 Numerical Quadrature (equallyspaced points).
 Adaptive Quadrature
 Richardson Extrapolation: Romberg.

13 
4/17 
Initial Val. Probs. for Ord. Diff. Equs (H: 9.19.3. A&G: 16.116.6. 
 
 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
 RungeKutta Methods
Review 
15 
4/24 
Last day of class 
XX 
5/01 
Enhanced Homework III (due Monday). 
  