Scientific Computation  - CS3210, Spring 2013 TR 1:10 - 2:25pm Roon: TBA Instructor:Joseph Traub Office Address: 456 CSBOffice Hours: Tuesday 2:30 - 3:00 pm, Thursday 3:30 - 4:00 pm and by appointmentEmail: traub@cs.columbia.edu TAs: TBA  Class Info: Required Text: Numerical Methods, Third Edition, Faires and Burden. I suggest you buy the 3rd 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 ProblemsMany problems in physics, chemistry, biology, engineering vision graphics, animations, weather predictions, etc. have continuous mathematical modelsExample: Ecosystems. Continuous problems usually have to be solved numerically The most important law in computing: Moore's lawWhy 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 equationBisection algorithm Pros/ConsNewton iterationError formulaPros/ConsTermination criteriaApplications of NewtonSquare root ReciprocalSecant algorithmFibonacci sequencePros/Cons Polynomial interpolation Spline interpolation Linear recurrences with constant coefficients Uncertainty, Undecidability Nonlinear recurrencesLogistic equationChaosStrange attractorsLimits to weather predictionButterfly effectFractals Univariate integrationWhy such an important problemTrapezoid moduleSimpson moduleComposite algorithm High dimensional integrationCurse of dimensionalityRandomizationMonte Carlo algorithmPros/Cons Dynamical systemsLinear ordinary differential equations (ODE)Nonlinear ODESeparation of variablesNumerical solutionEuler algorithmError of EulerPros/ConsHigher order TaylorRunge-Kutta Condition of problemWilkinson polynomial Implications of finite precision algorithm Stability of algorithm Backward error analysis