Math 128A
Numerical Analysis
Fall Quarter 2019
Instructor: Professor Bob Guy
Office: MSB 2136
Email: guy@math.ucdavis.edu
Phone: 754-9201
Class webpage: www.math.ucdavis.edu/~guy/teaching/128a
Text: A First Course in Numerical Methods, by Uri Ascher and Chen Greif. SIAM, 2011.
Electronic version available through the library from https://doi.org/10.1137/9780898719987

Teaching Assistants
Karry Wong, ucdwong@ucdavis.edu, MSB 3139
Carter Johnson, caljohnson@ucdavis.edu, MSB 2141

Office Hours
Monday, 4:15-5:30, Prof. Guy, MSB 2136
Tuesday, 1:00-2:00, Carter, MSB 2141
Wednesday, 11:30-12:30, Prof. Guy, MSB 2136
Wednesday, 3:00-5:00, Karry, Academic Surge 1029
Thursday, 1:00-2:00, Carter, MSB 2141
Thursday, 4:00-5:30, Prof. Guy, MSB 2136

Homework
You are encouraged to talk with your classmates about homework problems. You may work in groups with up to three students and turn in a single write-up for the group. All aspects of your write up must be clearly presented. Your writing should be clear and grammatically correct. Your codes must be thoroughly commented. All tables and figures must be appropriately labeled. You will be graded on the quality of your presentation.
Late homework will not be accepted!

Homework 1, due Friday, 10/11

Homework 2, due Friday, 10/25

Homework 3, due Wednesday, 11/13

Homework 4, due Tuesday, 11/26
noisy_signal.txt

Homework 5, due Friday, 12/6

Homework Instructions:

Programming
This class will require writing computer programs. You may use any language. All codes will be turned in and must be thoroughly commented. If you do not have a strong preference of language, it is recommended that you use MATLAB, because it is easy to use and very powerful. Further there are example MATLAB programs in the text, and I will occasionally give examples in MATLAB. Other languages that offer similar convenience include python, R, and julia. UCD students can obtain a free student license for MATLAB. Also, you can create a computer account in the math department at http://www.math.ucdavis.edu/comp/class-accts.

What we will cover
Roundoff error and floating point arithmetic (Ch 2)
Polynomial interpolation (Ch 10)
Piecewise polynomial interpolation (Ch 11)
Numerical differentiation (Ch 14)
Approximation theory (Ch 12)
Fourier transform, approximation & interpolation by trig polynomials (Ch 13)
Numerical integration (Ch 15)

Prerequisites
MAT21C (i.e. first year calculus) and any of ECS30, ECS32A, ENG6, EME5 (i.e. programming)

Grading
Your grade for the course will be based on your homework assignments, a midterm exam, and a final exam. Your lowest homework score will be dropped. The weights for each of these are as follows: the final. The weights for each of these are as follows:
Homework 50%
Midterm
15%
Final Exam
35%

Exam Dates
Midterm, Friday, November 1st.
Final exam, Monday, December 9th.


Announcements


Lectures/Calendar
Day Topics
25-Sept.
Lecture
Intro to class
Order of convergence
absolute/relative error
Example codes
riemann_ex1.m, riemann_ex1.py
riemann_ex2.m, riemann_ex2.py
27-Sept.
Lecture
Riemann sum example (see codes previous lecture)
Errors and floating point numbers (Chapter 2)
Example codes
rounding_unit_estimation.m, rounding_unit_estimation.py
30-Sept.
Lecture
Errors and floating point numbers (Chapter 2), continued
02-Oct.
Lecture
Round off examples (2.3)
Taylor polynomials/series
Introduce polynomial interpolation
04-Oct.
Lecture
Polynomial interpolation
Lagrange form
Theorems on existence, uniqueness, error bound
07-Oct.
Lecture
Theorems on uniqueness and error bound for interpolation
Barycentric form, evaluating Lagrange form efficiently
09-Oct.
Lecture
Newton form of the interpolating polynomial
Divided differences
11-Oct.
Lecture
Examples of interpolation, choice of points matters
Plots shown in class
Theorem on divided differences and accracy revisited
Codes
table10p5_interp_demo.m , divdif.m , evalnewt.m , newton_interp.m
table10p5_interp_demo.py, newton_poly.py
14-Oct.
Lecture
Interpolating with derivative values (10.7, briefly)
Begin Ch. 11, piecewise linear and piecewise Hermite cubic interpolation
Plots shown in class
16-Oct.
Lecture
piecewise Hermite cubic interpolation
Plots shown in class
begin cubic splines
18-Oct.
Lecture
cubic splines
21-Oct.
Lecture
linear system for cubic spline
accuracy of clamped splines
parametric curves
23-Oct.
Lecture
demonstration of splines and Hermite cubics in drawing programs
begin numerical differentiation (Ch. 14)
25-Oct.
Lecture
Taylor series to analyze/derive finite difference formulas
28-Oct.
Lecture
interpolation to derive finite difference formulas
effect of errors in numerical differentiation
30-Oct.
Lecture
discrete least squares approximation (Ch 6.1)
1-Nov.
Midterm
4-Nov.
Lecture
continuous least squares (Ch. 12.1)
begin orthogonal functions
Plots shown in class
6-Nov.
Lecture
orthogonal functions
Lagendre polynomials
8-Nov.
Lecture
Chebyshev polynomials
13-Nov.
Lecture
Chebyshev polynomials, min/max property
optimal points for polynomial interpolation
15-Nov.
Lecture
Trig polynomial approximation
Fourier series
18-Nov.
Lecture
Discrete Fourier transform
20-Nov.
Lecture
FFT
begin numerical integration
22-Nov.
Lecture
Numerical integration
25-Nov.
Lecture
Error analysis of numerical integration
27-Nov.
Lecture
Error analysis for Simpson's rule
Begin Gaussian quadrature
2-Dec.
Lecture
Gaussian quadrature
4-Dec.
Lecture
Gaussian quadrature examples
Adaptive quadrature
plots from class
6-Dec.
Review