Instructor  Manabu Machida 
Office  3836 East Hall 
Office hours 
MWTh 11am–12pm (and by appointment) 
Meeting times 
MWF 8am–9am at 4088 EH 
Prerequisites:
Differential equations (Math 216, 256, 286, or 316),
Linear algebra (214, 217, 417, or 419),
and a working knowledge of one highlevel computer language (Matlab).
No credit granted to those who have completed or are enrolled in
Math 371 or 472.
Background and Goals:
This is a survey of the basic numerical methods which are used to solve
scientific problems. The emphasis is evenly divided between the analysis of
the methods and their practical applications. Some convergence theorems and
error bounds are proven. The course also provides an introduction to MATLAB,
an interactive program for numerical linear algebra, as well as practice in
computer programming. One goal of the course is to show how calculus and
linear algebra are used in numerical analysis. There is software that can
be used as a black box, but in this course we will look under the hood and
see how the methods work.
Content:
Topics may include computer arithmetic, Newton's method for nonlinear
equations,
polynomial interpolation, numerical integration, systems of linear equations,
initial value problems for ordinary differential equations, quadrature,
partial pivoting, spline approximations, partial differential equations,
Monte Carlo methods, 2point boundary value problems, and the Dirichlet
problem for the Laplace equation.
Alternatives:
Math 371 is a less sophisticated version
intended principally for sophomore and junior engineering students.
Subsequent Courses:
The sequence Math 571–572 is mainly taken by graduate students,
but should be considered by strong undergraduates. Math 471 is good
preparation for
Math 571 and 572, although it is not prerequisite to these courses.
Textbook:
A Friendly Introduction to Numerical Analysis
by Brian Bradie
Pearson Prentice Hall, 1st ed., 2005
ISBN10: 0130130540, ISBN13: 9780130130549
Exams:

Midterm Exam: Oct 25 (Fri), 8:10am–9:00am
[materials between the first lecture and the fall break]

Final Exam: Dec 19 (Thu), 8:00am–10:00am
[cumulative]

In the midterm exams you will be allowed to bring in one side of
a US Letter size (8.5''x11.0'') paper with notes on it. For the final
you will be allowed both sides of a US Letter size paper
(or one side of two papers).

Calculators and other devices are not allowed in exams.

Exam dates are absolutely firm.
All students enrolled must plan to take exams at their scheduled times.
Grading Policy:

Homework 27% :
Homework will be assigned every 1–2 weeks. Some problems will require
Matlab programming. Each homework is due at the beginning of the class
on the due date. Late homework will not be accepted.
You are encouraged to discuss the course material and
the assigned homework problems with your colleagues, but
are responsible for writing up your own codes and solutions.

Quiz 3% : There will be one quiz.

Projects 10% : There will be two projects.

Midterm Exam, 20%; Final Exam, 40%.
Student Data Form:
Form
FAQ
Lecture Notes:
(see also Prof. Krasny's
lecture notes)
Syllabus:
1: 
Wed,  Sep  4 
Floating point arithmetic
(first day handout) 
2: 
Fri,  Sep  6 
Finite difference approximation of a derivative

3: 
Mon,  Sep  9 
First Matlab computation
(supplement)


4: 
Wed,  Sep  11 
The bisection method
(supplement)

5: 
Fri,  Sep  13 
Fixedpoint iteration
Homework Set 1 Due
(problems)

6: 
Mon,  Sep  16 
Newton's method


7: 
Wed,  Sep  18 
Review of linear algebra
Quiz

8: 
Fri,  Sep  20 
Gaussian elimination

9: 
Mon,  Sep  23 
Pivoting

10: 
Wed,  Sep  25 
Vector and matrix norms

11: 
Fri,  Sep  27 
Error analysis
Homework Set 2 Due
(problems)

12: 
Mon,  Sep  30 
LU factorization

13: 
Wed,  Oct  2 
Twopoint boundary value problem

14: 
Fri,  Oct  4 
Twopoint boundary value problem
(supplement)
Homework Set 3 Due
(problems)

15: 
Mon,  Oct  7 
Iterative methods: Jacobi method and GaussSeidel method

16: 
Wed,  Oct  9 
Convergence of iterations

17: 
Fri,  Oct  11 
Operation counts


Mon,  Oct  14 
Fall Study Break

18: 
Wed,  Oct  16 
SOR

19: 
Fri,  Oct  18 
SOR
Homework Set 4 Due
(problems)

20: 
Mon,  Oct  21 
Twodimensional boundaryvalue problems
(supplement)

21: 
Wed,  Oct  23 
Review



Fri,  Oct  25 
Midterm Exam
(solutions)


22: 
Mon,  Oct  28 
Rayleigh quotient

23: 
Wed,  Oct  30 
The power method and inverse power method


24: 
Fri,  Nov  1 
Polynomial approximation
Homework Set 5 Due
(problems)
Project 1 Due
(problems)

25: 
Mon,  Nov  4 
Polynomial interpolation

26: 
Wed,  Nov  6 
Newton's form

27: 
Fri,  Nov  8 
Optimal interpolation points
(supplement)

28: 
Mon,  Nov  11 
Error analysis

29: 
Wed,  Nov  13 
Error analysis

30: 
Fri,  Nov  15 
Piecewise linear interpolation
Homework Set 6 Due
(problems)

31: 
Mon,  Nov  18 
Spline interpolation


32: 
Wed,  Nov  20 
Numerical integration

33: 
Fri,  Nov  22 
Richardson extrapolation

34: 
Mon,  Nov  25 
Orthogonal polynomials

35: 
Wed,  Nov  27 
Gaussian quadrature
Homework Set 7 Due
(problems)
Project 2 Due
(problems)



Fri,  Nov  29 
Thanksgiving recess


36: 
Mon,  Dec  2 
Gaussian quadrature


37: 
Wed,  Dec  4 
Euler's method

38: 
Fri,  Dec  6 
Secondorder RungeKutta method
Homework Set 8 Due
(problems)

39: 
Mon,  Dec  9 
Fourthorder RungeKutta method


40: 
Wed,  Dec  11 
Review
Homework Set 9 Due
(problems)



Thu,  Dec  19 
Final Exam
(solutions)
