AMS 147 Computational Methods and Applications

Course description:
In this class, we discuss the numerical methods for solving problems in sciences and engineerings. We will learn how they work (and why they fail sometimes). We will learn how to implement these numerical methods using Matlab. The topics include
  • Iterative methods for solving non-linear equations
  • Golden search method for optimization
  • Floating point representation of real numbers, round-off error
  • Numerical differentiation and integration
  • Runge-Kutta methods for solving differential equations
  • Estimating error from two numerical solutions
  • Cubic spline interpolation (fitting to exact data)
  • Least square fitting (fitting to data with noise)
  • Fast Fourier transform
  • Conjugate gradient method for solving sparse linear systems
    • Lectures: TuTh 2:00-3:45pm at E2 194
    Instructor: Hongyun Wang (Email: hongwang AT ams DOT ucsc DOT edu)
    Office hours: TuTh 4:00-5:00pm at BE 153C
    Class web: http://www.soe.ucsc.edu/~hongwang/AMS147
    Lab sessions:
    Th 9:30am-12:00 at BE 109
    F 12:00-2:00pm and 3:30pm-5:00 at BE 109
    TA: Luis Antonio Acevedo-Arreguin (Email: arreguin AT soe DOT ucsc DOT edu)
    Textbook:
    There is no official textbook for this course. I will distribute my lecture notes electronically.
    Grading policy:
    Homework assignments + attending lectures: 50%; Course Project: 25%; Final Exam: 25%
    Important Dates:
    Attendance Poll: Tuesday 03/11/2008, 2:00-3:45 at E2 194.
    Final Exam: Tuesday 03/18/2008, 4:00-5:00 at E2 194.
    Useful links:
    Matlab manuals
    Lecture Notes
    Homework assignments
    For each assignment, follow the instructions given in the assignment. Some assignments have bonus parts. These bonus parts are optional and they might be difficult. So you should first finish the required part before start working on the bonus part.
  • Assignment #1 , due by the end of Friday 01/18/2008, submit one PDF file by email
  • Assignment #2 , due by the end of Friday 01/25/2008, submit one PDF file by email
  • Assignment #3 , due by the end of Friday 02/01/2008, submit one PDF file by email
  • Assignment #4 , due by the end of Friday 02/08/2008, submit one PDF file by email
  • Assignment #5 , due by the end of Friday 02/15/2008, submit one PDF file by email
  • Assignment #6 , due by the end of Wednesday 02/27/2008, submit one PDF file by email
  • Assignment #7, due by the end of Wednesday 03/05/2008, submit one PDF file by email
  • Assignment #8, (Optional)
    • Course project , due by the end of Tuesday 03/18/2007, submit one PDF file by email
    A sample code: Two-body problem

    Review probelms for the final exam