| 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 high-level 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 non-linear
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, 2-point 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 |
Fixed-point 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 |
Two-point boundary value problem
|
| 14: |
Fri, | Oct | 4 |
Two-point boundary value problem
(supplement)
Homework Set 3 Due
(problems)
|
| 15: |
Mon, | Oct | 7 |
Iterative methods: Jacobi method and Gauss-Seidel 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 |
Two-dimensional boundary-value 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 |
Second-order Runge-Kutta method
Homework Set 8 Due
(problems)
|
| 39: |
Mon, | Dec | 9 |
Fourth-order Runge-Kutta method
|
|
|
| 40: |
Wed, | Dec | 11 |
Review
Homework Set 9 Due
(problems)
|
|
|
|
Thu, | Dec | 19 |
Final Exam
(solutions)
|
