Teaching 2008 Fall Math 523


Math 523 (Numerical Analysis I)

Homework:

  • Homework Set 1: Hw1, Solution (Problem 1–4 due on Sep/05/2008; Problem 5–7 due on Sep/12/2008; Problem 8–12 due on Sep/22/2008.).
    • Note: For problem 8, there might be some algorithms which do not converge. If they do not converge, just say so.
  • Homework Set 2: Hw2, Solution (Problem 1–3 due on Oct/03/2008; Problem 4–5 due on Oct/10/2008; Problem 6–10 due on Oct/17/2008).
    • Note: Problem 6–10 will be counted as your midterm (20% of your final score). No discussion on these problems.
  • Homework Set 3: Hw3, Solution (Problem 1–4 due on Oct/31/2008).
  • Homework Set 4: Hw4, Solution (Problem 1–4 due on Nov/17/2008).
    • Note: For problem 4, use initial guess (0,2) or (0,0).
    • Here is a zip file which contains Matlab codes for this homework. (The extension is named as .pdf for security reasons. You need to change it back to .zip!)
  • Homework Set 5Hw5Solution (Problem 1–4 due on Dec/05/2008; Problem 5–7 due on Dec/12/2008).

Final Project:

  • Project description
  • A sample project proposal
  • Project topic due time: Nov/21/2008
  • Project report due time: Dec/19/2008
  • Topics:
    • Solving Cahn-Hillard equation with composition dependent mobility
    • Method of Moments (MoM) and Finite Difference Time Domain (FDTD) methods are two methods are used in computational electromagnetics
    • Study of 2-D laminar, viscous, supersonic flow over a flat plate with zero angle of incidence using finite difference space discretization scheme and Runge-Kutta time marching schemes
    • Magma chamber volume change estimates using noisy dilatometer measurements
    • Numerical study of some minimizer problems using quasi-Newton schemes and line search methods
    • Numerical solution of both the laminar and turbulent boundary layers (steady state case) over the flat plate using the finite differencing
    • Multidimensional quadrature and its application in Brownian Coagulation
    • Preconditioning conjugate gradient methods with application for elliptic PDEs
    • Numerical optimization algorithm for RNA secondary structure prediction via free energy minimization
    • Study of unsteady convection diffusion equation
    • Numerical Solution of Parabolic Equation using LU decomposition


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