## 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.

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__**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.

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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__