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Spring Semester 2011

Math 170C (Introduction to Numerical Analysis: ODEs)

Syllabus

Links:

Summary:
Many of the advances of modern science have been made possible only through the sophisticated use of computer modeling. The mathematical foundation of the computer modeling techniques now used in all areas of mathematics, engineering, and science is known as Numerical Analysis. The Math 170ABC series at UCSD provides an introduction to the exciting field of numerical analysis, which is also sometimes referred to as Computational Mathematics or Scientific Computing.

Math 170C deals primarily with the numerical solution of ordinary differential equations (ODEs). In 170C we will also study related numerical techniques for approximating the derivatives and integrals of functions in a stable and accurate way. Previous quarters dealt with numerical linear algebra (170A) and nonlinear equations and numerical approximation theory (170B), and we will have occasion to use these ideas to develop new techniques in 170C. The textbook for the course will be as listed below.


Contact Information:
Instructor: Tanya Shingel
Email: tshingel@math.ucsd.edu
Office hours:   Mo,Thu 10:00-11:00am or by appointment in AP& M 5747

TA: Jonny Serencsa
Email: jserencs@math.ucsd.edu
Section:    Tu 1:00-1:50pm in Center 218
Office hours:   We 1:00-3:00pm or by appointment in AP& M 5720

Time and Place:
Lectures:   MWF 3:00-3:50pm in AP& M 2402

Recommended Textbook:
  • D. Kincaid, W. Cheney: Numerical Analysis: Mathematics of Scientific Computing, Third Edition, AMS Press, 2002.

Additional Reading:
  • A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics, Springer, 2000.
  • J. Stoer, R. Bulirsch: Introduction to Numerical Analysis, 3rd edition, Texts in Appl. Math., vol. 12, Springer, 2002.
  • E. Süli, D. Mayers: An Introduction to Numerical Analysis, Cambridge University Press, 2003.

Homework:
There will be five homework assignments throughout the quarter. The homework will be due in class on Wednesday in the weeks 3, 4, 6, 8 and 10. All homework assignments will count towards the grade. Late HW will not be accepted.

A MATLAB code should be sent in a single email to Jonny Serencsa .

Short list of things you may take into account when doing a MATLAB question:

  • The code you write should in general not be all in one file. You should separate it in more files (in a meaningful way).
  • When you write the code, please add comments where you feel the TA may get confused with what you are doing.
  • Every .m file you submit should have a short comment at the beginning (before any code) saying something about the purpose of that file.
  • There should be a file called run_tests.m that will, as the name suggests, run all the tests and produce the graphs you have to show. This file should not be the only file you submit.
  • Your code must compile. If that is not the case, or files are missing from your submission, points will be subtracted.

Homework is your individual work. You may consult other current MATH 170C students to clarify their approach to a problem. However, as a general guide, you should be able to independently reproduce any solution that is submitted as homework. Copying of solutions is not permitted and will be considered as a violation of these guidelines.


Grading:
  • The final grade will be computed from the weighted average of percentages of maximal scores with the weights

    Homework: 30%
    Midterm Exam:   30%
    Final Exam: 40%

    according to the following table:

    Cutoff score:   95%  90%  85%  80%  75%  70%  65%  55%  50%  less than 50% 
    Grade:   A+ A A- B+ B B- C+ C C-     F


Class Schedule (Topics are subject to change)

03/28/2011: Polynomial interpolation. Largange interpolation formula.
03/30/2011: Polynomial interpolation (cont.). Error in polynomial interpolation.
04/01/2011: Polynomial Interpolation (cont.). Divided differences. Newton interpolation formula.
04/04/2011: Numerical differentiation. Richardson extrapolation.
04/06/2011: Numerical integration based on interpolation.
04/08/2011: Numerical integration based on interpolation (cont.). Trapezoidal rule. Simpson's rule.
04/11/2011: Romberg integration.
04/13/2011: Adaptive quadrature.
04/15/2011: Gaussian quadrature.
04/18/2011: Basic theory of ordinary differential equations. Existence and uniqueness of solutions.
04/20/2011: Euler's method.
04/22/2011: Taylor-series method for ODEs.
04/25/2011: Runge-Kutta methods.
04/27/2011: Review for the midterm exam.
04/29/2011: Midterm Exam.
05/02/2011: Multistep methods. Adams-Bashforth formula.
05/04/2011: Multistep methods (cont.). Adams-Moulton formula.
05/06/2011: Multistep methods (cont.). Local and global errors: stability.
05/09/2011: Systems of higher-order ODEs.
05/11/2011: Systems of higher-order ODEs (cont.). Extensions of the methods.
05/13/2011: Systems of higher-order ODEs (cont.). Extensions of the methods.
05/16/2011: Introduction to boundary-value problems in ODEs.
05/18/2011: Boundary-value problems. Shooting methods.
05/20/2011: Boundary-value problems. Shooting methods (cont.).
05/23/2011: Boundary-value problems: finite difference methods.
05/25/2011: Boundary-value problems: finite difference methods (cont.).
05/27/2011: Linear systems of autonomous ODEs.
05/30/2011: Memorial Day.
06/01/2011: Linear systems of autonomous ODEs (cont.).
06/03/2011: Review for the final exam.
06/08/2011: Final Exam.



Last modified: 2011/05/31
This page: http://ccom.ucsd.edu/~tshingel/NumericalAnalysis.html
Tanya Shingel ( tshingel@math.ucsd.edu)