CSW3210




	Scientific Computation - CS3210, Spring 2013 TR 1:10 - 2:25pm Roon: TBA Instructor:Joseph Traub Office Address: 456 CSB Office Hours: Tuesday 2:30 - 3:00 pm, Thursday 3:30 - 4:00 pm and by appointment Email: traub@cs.columbia.edu TAs: TBA Class Info: Required Text: Numerical Methods, Third Edition, Faires and Burden. I suggest you buy the 3^rd edition used. Detailed information about homeworks, solution sets, handouts, grades etc. will be posted in Courseworks. Grading 30% homework 30% midterm, 40% final 10% extra credit homework You are responsible for the material covered in: lectures, readings and homeworks. TOPICS Continuous Problems Many problems in physics, chemistry, biology, engineering vision graphics, animations, weather predictions, etc. have continuous mathematical models Example: Ecosystems. Continuous problems usually have to be solved numerically The most important law in computing: Moore's law Why Moore's law is ending for current technology and what can be done about it. The world's fastest computers Scaling laws Brief review of calculus results we'll need. Solutions of nonlinear equation Bisection algorithm Pros/Cons Newton iteration Error formula Pros/Cons Termination criteria Applications of Newton Square root Reciprocal Secant algorithm Fibonacci sequence Pros/Cons Polynomial interpolation Spline interpolation Linear recurrences with constant coefficients Uncertainty, Undecidability Nonlinear recurrences Logistic equation Chaos Strange attractors Limits to weather prediction Butterfly effect Fractals Univariate integration Why such an important problem Trapezoid module Simpson module Composite algorithm High dimensional integration Curse of dimensionality Randomization Monte Carlo algorithm Pros/Cons Dynamical systems Linear ordinary differential equations (ODE) Nonlinear ODE Separation of variables Numerical solution Euler algorithm Error of Euler Pros/Cons Higher order Taylor Runge-Kutta Condition of problem Wilkinson polynomial Implications of finite precision algorithm Stability of algorithm Backward error analysis