
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 RungeKutta
 Condition of problem
Wilkinson polynomial
 Implications of finite precision algorithm
 Stability of algorithm
 Backward error analysis

