Introduction to Scientific Computing

Introduction to Scientific Computing

Math 551 Summer 2019

Office: 1526 LGRT
Phone: (413) 545-2817
Office Hours: TBD
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

Grading: The grading of the course will be as follows. There will be a final exam worth 40%, one midterm worth 35%, and homework (lowest 1 dropped) worth 25%.

Grading: Midterm Monday, June 10th; Final Friday, June 28th

Free MATLAB software: Here is a link to the OIT MATLAB website.

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

Additonal Materials:

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
5/20 First day of class. Taylor polynomials and Taylor series.
Assigned HW1 , due 5/24/19.
Here are the m-files fp_example.m and graphsetup.m .
Read sections 1.1-1.3 and 2.1-2.2

5/23 Conditioning, stabilty, and finite precision.
Assigned HW2 , due 5/30/19.
Read sections 3.1-3.3.

5/28 Roots of nonlinear functions and the bisection method.
Here is the m-file my_bisect.m .

5/30 Fixed point methods and Newton's method.
Assigned HW3 , due 6/6/19.
Here is the m-file my_newton.m , and a handout on order of convergence.
Read sections 5.1-5.3 and 4.1-4.2.

6/6 Pivoting and error analysis.
Assigned HW4 , due 6/14/19.
Here is the m-file mylu_nop.m .

6/11 Condition number.
Read sections 10.1-10.3.

6/19 Error in polynomial interpolation.
Assigned HW5 , due 6/21/19.
Here is the m-file chebyex.m .
Read sections 10.4-10.6.

6/21 Numerical quadrature.
Assigned HW6 , due 6/26/19.

**Class Happenings**
5/20	First day of class. Taylor polynomials and Taylor series. Assigned HW1 , due 5/24/19. Here are the m-files fp_example.m and graphsetup.m . Read sections 1.1-1.3 and 2.1-2.2
5/23	Conditioning, stabilty, and finite precision. Assigned HW2 , due 5/30/19. Read sections 3.1-3.3.
5/28	Roots of nonlinear functions and the bisection method. Here is the m-file my_bisect.m .
5/30	Fixed point methods and Newton's method. Assigned HW3 , due 6/6/19. Here is the m-file my_newton.m , and a handout on order of convergence. Read sections 5.1-5.3 and 4.1-4.2.
6/6	Pivoting and error analysis. Assigned HW4 , due 6/14/19. Here is the m-file mylu_nop.m .
6/11	Condition number. Read sections 10.1-10.3.
6/19	Error in polynomial interpolation. Assigned HW5 , due 6/21/19. Here is the m-file chebyex.m . Read sections 10.4-10.6.
6/21	Numerical quadrature. Assigned HW6 , due 6/26/19.

Homework Solutions: