Math104A
Introduction to Numerical Analysis
http://www.math.ucsb.edu/~hdc/teaching/Math104A
Announcement: No lecture on Oct 15. No
office hours on Oct 13 and Oct 15.
Class:
TR 9:30-10:45 a.m. 387 101.
Instructor:
Prof. Hector
D. Ceniceros.
SH 6710, Email: hdc@math.ucsb.edu,
phone: 893-3462 . Office Hours: TR 10:45-Noon.
TA:
Daniel Salazar Office hours Thursday 2-3pm and Mathlab hours Thursday
5-7pm.
Course description:
This is an introductory course on numerical methods for
the following problems: finding zeros of functions in one variable,
i.e.
obtaining approximate solutions to certain equations of the form
f(x)=0.
Interpolation and extrapolation: constructing a smooth curve (a
polynomial
or a spline) that connects a set of data points. Numerical
differentiation
and integration, and approximate solutions of initial value problems of
ordinary differential equations. We will analyze how, why, and when the
numerical methods work and provide error bounds for their
approximations.
Textbook:
Numerical Analysis by R. L. Burden and J. D. Faires.
Brooks/Cole Publishing Company, 8th edition. We will cover (partially
or completely ) Chapters 1-5.
Prerequisites:
Math 5 A, B, and C or equivalent. Knowledge of a
computer
language suitable for numerical computing. Matlab is
recommended but
FORTRAN, C or C++ can also be used. Octave
is also a freeware
alternative to Matlab. For matlab tutorial see this link.
Homework assignments:
Homework will be assigned every week and is
due a week after at the beginning of the lecture or as
instructed.
Some homeworks will include programming assignments. Please no late
homework.
Grade:
Homework 30%. Midterm 30 % (October 27, 9:30-10:45am).
Final 40 % (December 9, Wednesday, 8-11 am). There will be no make-up exams.
Homework 1 (Due Oct
8)
1. Read the list
(compiled by Prof. Doug Arnold) of disaters due to inaccurate numerical
computing and write a summary of each disaster.
2. Section 1.2: do problems 1,3, 4.
3. Section 2.1: Implement (i.e write a computer code) of the Bisection
Method (Algorithm 2.1) and use the code to do problems 4, 7 , 14 .
Hand in your code as well as the results from the runs
from which you got the solution to the problems. Present your work in a
clear and organized manner.
Homework 2 (Due Oct
22)
Section 2.3 Implement Newton's method (Algorithm 2.3) and use it
to do problem 6. Do also problem 15. Turn in both the code and a
printout of your results.
Section 2.4: Do problems 6, 7, 9, and 10.
Practice
Midterm
Homework 3 (Due Nov
12)
Section 3.2 Do problems 1, 10, 11, 16, and 17.
Section 3.4: Do problems 1 and 2. Write an appropriate a code
(Algorithm 3.4) to do problem 31.
Solutions
to the Midterm
Homework 4 (Due Nov 19)
Section 4.1 Do problems 1, 2 , 21.
Section 4.2 Do problems 1, 5, 8.
Section 4.3 Do problems 2, 4, 6, 8, 13, 16.
Section 4.4 Do problem 8 (You need to write a code and turn it in
together with a printout of the results for this problem)
Homework 5 (Due Dec 3)
Section 4.5 Do problems (write code) 2, 6, 7.
Section 5.1 Do problem 1
Section 5.2 Implement Euler's method to do prob. 10
Section 5.4. Implement RK 4 to do prob. 15
Practice Final
Problems