WEEK 
DATE 
TOPICS 
1 
1/19 
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 
1/24 
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 26

3 
1/31 
... 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 
2/07 
... Linear equations continued 
 
 Sensitivity and Conditioning.
 Methods: Gaussian Elimination and Back Substitution.

5 
2/14 
Nonlinear Equations  Systems (H: 5.45.6, [A&G: Chap 9]) 
 
 HW2 due Mon Feb 14.
 Partial Derivatives: gradients, Jacobians.
 Fixed Point Methods. Newton's method.

6 
2/21 
Polynomial Interpolation (H: 7.17.3. A&G: 7.17.3) 
 
 Existence and Uniqueness
 Methods: undetermined coefs.

6 
2/22 
Enhanced Homework I (out Monday, due Tuesday). 
  
7 
2/28 
... Interpolation continued 
 
 Methods: Lagrange polynomials. divided differences.

...  ...  Splines (H: 7.4. A&G: 11.3, 11.6) 
 
 Piecewise polynomial interpolation: splines.
 Twodimensional interpolation/splines (from notes).

=== 
3/07 
SPRING BREAK 
 
 Romp in the virtual sand.

8 
3/14 
Linear Least Squares (H: 3.13.2. A&G: 6.1) 
 
 HW3 due Fri Mar 04.
 Existence and Uniqueness
 Normal equations.

9 
3/21 
Unconstrained Optimization Problems (H: 6.16.5. A&G: Chap 9, 3.5,9.29.3) 
 
 First & second order conditions for optimality in 1D, gradients, Hessians.
 Onedimension: Golden Section Search.
 Existence and Uniqueness: coercive and convex functions
 Conditioning

10 
3/28 
Unconstrained Optimization Problems (continued) 
 
 Conditioning
 First & second order conditions for optimality (multidim): gradients, Hessians.
 Multidimensional methods: steepest descent, Newton, BFGS.
 Line Search

11 
4/04 
Constrained Optimization Problems (H: 6.7. A&G: 9.3) 
 
 HW4 due Mon Apr 04.
 Conditioning
 First & second order conditions for optimality (multidim): gradients, Hessians.
 Equality constraints, inequality constraints
 First Order conditions for optimality: KKT conditions

12 
4/11 
Enhanced Homework II (out Monday, due Tuesday). 
  
12 
4/11 
Constrained Optimization Problems (continued) 
 
 Penalty & barrier methods. (maybe dual ascent methods?)
 Linear Programs.

13 
4/18 
Numerical Integration and Quadrature (H: 8.18.4, 8.7. A&G: 15.115.2,15.415.5) 
 
 HW5 due Mon Apr 18
 Existence and Uniqueness
 Numerical Quadrature (equallyspaced points).
 Adaptive Quadrature
 Richardson Extrapolation: Romberg.

14 
4/25 
Initial Val. Probs. for Ord. Diff. Equs (H: 9.19.3. A&G: 16.116.6.) 
 
 Existence and Uniqueness, stability of solutions
 Linear ODEs
 Methods: Euler, Backward Euler.
 RungeKutta Methods
 Accuracy and Stability: local vs global truncation error

15 
5/02 
review 
  
Final 
5/09 
Enhanced Homework III (out Monday, due Tuesday). 
  