Office: 1526 LGRT

Phone: (413) 545-2817

Office Hours: M 3-4:30, W 11:45-1:15

Email: johnston at math umass edu

**Textbook:** * A First Course in Numerical Methods*, by
Ascher & Greif (SIAM)
(UMass Library FREE ebook)

**Course description:** The course will introduce foundational numerical
methods used for problems that arise in many scientific fields.
Properties such as accuracy of methods, their stability and efficiency
will be considered. Students will gain
practical programming experience in implementing the methods using MATLAB,
which will be taught through incrasingly complex codes over the term, with
examples in class and students homework assignments.
From time to time we will also discuss practical considerations of
implementing these methods on modern computer architectures using C, C++ or Fortran.
Today's average smartphone can computationally crush a 1990's era Cray C90,
which cost $10 million at the time ($18 million in today's $) for sixteen
244Mhz vector processors and 8GB of RAM.

**Topics:** We will cover the following topics (not necessarily in this order):

- Finite Precision Arithmetic and Error Propagation
- Root Finding
- Linear Systems of Equations
- Interpolation and Approximation of Functions
- Numerical Differentiation and Integration
- Basic Numerical Methods for Differential Equations

**Access to MATLAB in OIT Labs:** Here is a link to the
OIT Computer Classrooms website.

**MATLAB Help:** Here are a few PDF files and links
for help with MATLAB:

- MATLAB Quick Reference (PDF)
- MATLAB Plotting Guide (PDF) (from MSCC, University of Washington, 1996)
- MATLAB Help Desk at the MathWorks site.

**OCTAVE Homepage:**
Octave is an open source program that is mostly compatible with MATLAB.

**"Careful with That Axe, Eugene": **

- Collection of Software Bugs, by Thomas Huckle
- Disasters Attributable to Bad Computing, by Doug Arnold

- Origins of MATLAB , by Cleve Moler
- Essay on Numerical Analysis, by Nick Trefethen
- Scientific Programming and Computer Architecture, by Divakar Viswanath
- Scientific Programming and Computer Architecture UMass Lecture, by Divakar Viswanath

** Class Happenings **
1/22
First day of class. Taylor polynomials and Taylor series.

Here are the m-files fp_example.m
and graphsetup.m .

Read sections 1.1-1.3 and 2.1-2.2
1/29
Assigned HW1 , due 2/7/19.

M-files: taylor_exp_ex.m
taylor_exp_ex.m ,
fp_example_h_h2.m
1/31
Conditioning, stability, and finite precision
2/7
Roots of nonlinear equations and the bisection method.

Read sections 3.1-3.3.

Assigned HW2 , due 2/19/19
to my office or mailbox by 4:30pm.

2/12
Fixed point methods.

M-file: my_bisect.m
2/14
More on fixed point methods.

Read section 3.4: Newton's method and variants.

Assigned HW3 , due 2/28.

2/21
More on Newton's method.

M-file: my_newton.m
2/26
Order of convergence and the secant method.

Handout: convorder.txt

Assigned HW4 , due 3/5.

2/28
The order convergence of the secant method is the Golden Ratio.

M-file: my_secant.m
3/5
Intro to Numerical Linear Algebra.

Read sections 4.1-4.2
and 5.1-5.3.
3/21
Assigned HW5 , due 2/28/19.

M-files: mylu_nop.m ,
mylu_solve_nop.m
3/28
Norms, conditioning, and 2-point boundary value problems.

Assigned HW6 , due 4/4.

4/2
Iterative methods for linear systems.

M-files: my_lu.m ,
my_trilu.m ,
my_trilu_solve.m
4/10
Polynomial interpolation.

Read sections 10.1-10.3.

Assigned HW7 , due 4/23/19.

** Homework Solutions: **