MATH 270B Numerical Approximation and Nonlinear Equations

TTh 12:30pm-1:50pm, APM 2402.

Prof. Melvin Leok
Office: AP&M 5763
Email: mleok@math.ucsd.edu
Office Hours: T 10:00am-10:50am, Th 10:30pm-11:20pm, or by appointment.

Jingwen Liang
Office: AP&M 6442
Email: jil343@ucsd.edu
Office Hours: M 5-6pm, W 5-6pm, AP&M 6442.

The midterm will be in class on Tuesday, February 19. It will cover all the material up to and including B-splines. You are allowed one sheet (letter sized, both sides) of handwritten notes.
The final will be on Tuesday, March 19, 11:30am to 2:30pm. It will be comprehensive, and you are allowed two sheets (letter sized, both sides) of handwritten notes.
The resources below are password protected with the user name ma270b, and the password is the first 4 digits of:
$\sqrt{6\sum_{n=1}^\infty}{1}{n^2}}$ .

This course focuses on numerical methods for solving nonlinear equations and optimization problems, and on classical and modern approximation theory as needed for analyzing numerical methods.

MATH 270A or consent of instructor. Programming experience in any language, e.g., C/C++, FORTRAN, MATLAB.

A Theoretical Numerical Analysis: A Functional Analysis Framework, 3rd Edition, Texts in Applied Mathematics
Kendall Atkinson and Weimin Han, Springer, 2009. ISBN: 978-1441904577 [ Electronic version | SpringerLink | Amazon ]
Supplementary reference
Numerical Analysis: Mathematics of Scientific Computing, Third Edition
David Kincaid and Ward Cheney, AMS Press, 2002. ISBN: 978-0-8218-47886 [ Electronic version | Amazon ]

HW1: Exercises (Atkinson and Han) 3.1.2, 3.1.3, 3.1.4, 3.1.6.
Due Thursday, January 24, 2019 (Due date extended from Tuesday due to MLK Day)
For 3.1.3, use the coordinate change from cartesian coordinates to polar coordinates to transform bivariate polynomials to trigonometric polynomials (when restricted to the unit circle).
HW2: Exercises (Atkinson and Han) 3.2.1, 3.2.3, 3.2.5, 3.2.6, 3.2.8.
Due Thursday, January 31, 2019.
HW3: Exercises (Kincaid and Cheney) 6.2.24, 6.3.1, 6.4.5, 6.4.7, 6.5.1, 6.5.2 [ PDF ]
Due Thursday, February 7, 2019.
HW4: Exercises (Kincaid and Cheney) 6.5.3, 6.5.13, 6.5.19, 6.6.2 [ PDF ]
Due Thursday, February 14, 2019.
HW5: Exercises (Atkinson and Han)
3.4.4, 3.4.6, 3.5.5, 3.5.9, 3.6.3, 3.6.5 Due Thursday, February 28, 2019.
HW6: Exercises (Atkinson and Han)
4.1.1, 4.3.2, 4.3.4, 4.4.1, 4.4.4 Due Thursday, March 7, 2019.
HW7: Exercises (Atkinson and Han)
5.1.3, 5.2.2, 5.3.1, 5.3.12, 5.3.16, 5.4.1 Not graded, but the topics will be tested on the final.

Your grade in the course is based on homework (25%), a midterm exam (25%), and a final exam (50%).