## Last Revised 01/20/21 (provisional schedule, dates subject to change)

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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).