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WEEK	DATE	TOPICS
1	1/20	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	1/25	Scalar Nonlinear Equs (Chap 5, secs 1, (2), 4 ?)
		Existence and Uniqueness Sensitivity and Conditioning. backward error vs forward error Methods: Bisection, Newton, Secant. HW0 due Wed Jan 27
3	2/01	... 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	2/08	... Linear equations continued
		Sensitivity and Conditioning. Methods: Gaussian Elimination and Back Substitution.
5	2/15	Nonlinear Equations -- Systems (Chap 5, secs 4-6)
		HW1 due Mon Feb 15. Partial Derivatives: gradients, Jacobians. Fixed Point Methods. Newton's method.
6	2/22	Polynomial Interpolation (Chap. 7, secs 1-3)
		Existence and Uniqueness Methods: undetermined coefs.
6	2/22	Enhanced Homework I (out Monday, due Tuesday).
7	3/01	... Interpolation continued
		Methods: Lagrange polynomials. divided differences.
...	...	Splines (Chap 7. sec 4)
		Piecewise polynomial interpolation: splines. Two-dimensional interpolation/splines (from notes).
8	3/08	Linear Least Squares (Chap 3, secs 1, 2)
		HW2 due Mon Mar 08. 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	3/15	... 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
10	3/22	Constrained Optimization Problems (Chap 6, sec 7)
		HW3 due Mon Mar 22. Equality constraints, inequality constraints First Order conditions for optimality: KKT conditions
11	3/29	Constrained Optimization Problems (Chap 6, sec 7)
		Penalty & barrier methods. (maybe dual ascent methods?) Linear Programs.
10	3/29	Enhanced Homework II (out Monday, due Tuesday).
===	4/05	Spring Break
		Romp in the virtual sand.
12	4/12	Numerical Integration and Quadrature (Chap 8, secs 1-4,7)
		HW4 due Mon Apr 19 Existence and Uniqueness Numerical Quadrature (equally-spaced points). Adaptive Quadrature Richardson Extrapolation: Romberg.
13	4/19	Initial Val. Probs. for Ord. Diff. Equs
		Existence and Uniqueness, stability of solutions Linear ODEs Methods: Euler, Backward Euler.
14	4/26	... ODEs continued
		HW5 due Wed Apr 28. Accuracy and Stability: local vs global truncation error Runge-Kutta Methods
15	5/03	Enhanced Homework III (out Monday, due Tuesday).

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