Adv Num Methods Optimiz & Stat

Catalog description

This course introduces practical numerical methods for engineers and an applied statistics module. Its goals are (1) build strong intuition for error, conditioning, and algorithmic stability; and (2) develop practical fluency implementing core solvers for large sparse linear/nonlinear systems, gradient-based optimization, uncertainty quantification, and a focused finite-difference PDE block (2D/3D). Modules tentatively included in this course are: (1) statistical estimation for computation; (2) gradient methods (steepest descent, BFGS/L-BFGS); (3) Monte Carlo with variance-reduction; (4) geometry optimization (L-BFGS/CG/FIRE); and (5) finite-difference PDEs (2D/3D). Prerequisites: Calculus I-III (Math 224/5/6/7 and 323) or equivalent; Ordinary Differential Equations (MATH 324) or equivalent; Engineering Computational Methods (ME 303) or equivalent; MATLAB will be used for course assignments and case studies. Offered in the Spring.