Office: 1526 LGRT
Phone: (413) 545-2817 (good luck!)
Email: johnston at math umass edu

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

2/2	First day of class:   Video m-files: fp_example.m , graphsetup.m , taylor_cos_ex.m , taylor_exp_ex.m Read Sections 1.1-1.3 in the book.
2/4	Taylor Polynomials:   Video   PDF Assigned HW1 , due 2/17.
2/9	Finite Differences & MATLAB:   Video   PDF m/tex-files: save2pdf.m , save2jpg.m , hw1_answered.tex
2/11	More on Finite Differences & LaTex:   PDF
2/16	Errors and Stability:   Video   PDF Assigned HW2 ( PDF , Tex ) due 2/25.
2/16	Stability and Floating Point Sysytems:   Video   PDF
2/23	Machine eps, Roots of Nonlinear equations, Bisection:   Video   PDF Assigned HW3 ( PDF , Tex ) due 3/4.
2/25	Bisection:   Video   PDF m-file: my_bisect
3/2	Fixed-point methods.   Video   PDF
3/4	More on Fixed-Point methods:   Video   PDF Assigned HW4 (PDF, Tex ) due 3/18.
3/9	EVEN More on Fixed-Point methods:   Video   PDF
3/16	Newton's method:   Video   PDF m-file: my_newton MODIFIED HW4 (only 4 problems) (PDF, Tex ) due 3/18.
3/18	More Newton's method then Ax = b:   Video   PDF Assigned HW5 (PDF, Tex ) due 3/26. Read Sections 5.1-5.2 in the book.
3/23	Ax = b and the LU decompostion:   Video   PDF
3/25	GE, LU and operation counts:   Video   PDF Assigned HW6 (PDF, Tex ) due 4/2.
3/30	Pivoting:   Video   PDF
4/1	Efficient Implementation of Pivoting:   Video   PDF
4/8	Errors and Norms:   Video   PDF
4/13	Iterative methods for Ax=b:   Video   PDF Assigned HW7 (PDF, Tex ) due 4/21.
4/15	Jacobi, Gauss-Seidel and Error analysis:   Video   PDF
4/22	Spectral theory for iterative methods:   Video   PDF Assigned HW8 (PDF) due 4/30.
4/27	More spectral theory and SOR:   Video   PDF
4/29	Iterative methods codes and examples:   Video   PDF Assigned HW9 (PDF, Tex ) due 5/12. m-file: Jacobi & Gauss-Seidel code
5/4	Last class:   PDF