Math 269B, Lecture 1, Winter 2005

Advanced Numerical Analysis

Lecture Meeting Time: MWF 2.00PM - 2:50PM.
Lecture Location: MS 5138

Instructor: Luminita A. Vese
Office: MS 7620D
Office hours: M 3-4pm, W 3-4, F 4-5pm.
E-mail: lvese@math.ucla.edu

Discussion Section: Thursday, 3.00PM - 3.50PM, MS 5138

Teaching Assistant: Jason Chung.
Office: IPAM Building.
Office hours: TBA.
E-mail: senninha@math.ucla.edu

Required Textbook: (placed on reserve for 2 hours/overnight at SEL Library).
K.W. Morton and D.F. Mayers, "Numerical Solution of Partial Differential Equations", Cambridge University Press, 2003.

Recommended Textbooks:
  • Strikwerda, John C., "Finite difference schemes and partial differential equations", Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1989, Series: The Wadsworth & Brooks/Cole mathematics series.
  • H.-O. Kreiss, and J. Oliger, 1973: Methods for the approximate solution of time dependent problems, WMO/ICSU Joint Organising Committee, GARP Publications Series No. 10, 107 pp.
  • R.D. Richtmyer and K.W. Morton (1967), Difference Methods for Initial-Value Problems, New York : Interscience Publishers.
  • B. Gustafsson, H.-O. Kreiss and J. Oliger, Time dependent problems and difference methods, A Wiley-Interscience Publication, 1995.
  • H.-O. Kreiss, H.U. Busenhart, Time-dependent Partial Differential equations and Their Numerical Solution, Birkhauser, Lectures in Mathematics, ETH Zurich, 2001.

    Topics:
    - Numerical solutions for initial and boundary value problems (time-dependent partial differential equations).
    - Numerical solution for elliptic, parabolic, and hyperbolic partial differential equations: stability, consistency, convergence, nonlinear problems.
    - Linear algebra considerations.

    Requisites: courses 115A, 135A, 151A, 151B.

    SYLLABUS TBA

    Useful Links:
  • Virtual Office Hours
  • PIC Lab: Boelter Hall 2817 and Mathematical Sciences 3970
    http://www.pic.ucla.edu/piclab/
  • MATLAB Documentation (thanks to Prof. C. Anderson, UCLA)
  • Class Web Page: http://www.math.ucla.edu/~lvese/269b.1.05w/
  • Numerical Analysis Qualifying Exam
  • Numerical Recipes
  • Getting started with MATLAB

    Homework Policy: Homework assignments involving both theoretical and computational exercises will be collected every Friday (in lecture).

    Examinations: One midterm exam and one final exam.
    Midterm Exam: Thursday, February 17 (in discussion section).
    Final Exam: Wednesday, March 16, 2-5pm, MS 5138.
    The examinations are closed-book and closed-note.
    No exams at a time other than the designated ones will be allowed (exceptions for illness with document proof, or emergency).

    Grading Policy: HW 40%, Midterm 20%, Final 40%

    Weekly Homework Assignments:

    HW #1 (due Friday, January 14) HW1.pdf

    HW #2 (due Friday, January 21) HW2.pdf

    HW #3 (due Friday, January 28) HW3.pdf

    HW #4 (due Monday, February 7) HW4.pdf

    HW #5 (due Monday, February 14) HW5.pdf

    REMINDER: MIDTERM EXAM on Thursday February 17, 3-4pm.
    Practice problems for the midterm

    HW #6 (due on: Friday, February 25) HW6.pdf

    HW #7 (due on: Friday, March 4) HW7.pdf

    HW #8 (due on: Monday, March 14 or Wednesday, March 16) HW8.pdf
    (no late homework accepted)

    Practice problems for the final PracticeFinal.pdf