All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly. This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the Honor Code, students are obligated to report any such activities to the Instructor.
Spring 2012 Course Syllabus:
Math 440
Course
Title: |
Advanced
Applied Numerical Methods |
Textbook: |
Introduction to Computation and
Modeling for Differential Equations,
Lennart Edsberg.
Textbook Homepage containing
misprints, Matlab programs, and exercise solutions |
Supplementary Text |
Elementary Numerical Analysis,
Atkinson & Han (Math 340 book) |
Prerequisites: |
Math 331 (PDE) and Math 340 (Numerics) |
Note:
This webpage will not be updated. An additional webpage with homework
solutions and up-to-date guidelines for Computational
Lab assignments is located
here.
Course Objectives:
The aim of the course is to
teach computational methods for solving ordinary and partial differential
equations. This includes the construction, application and analysis of basic
computational algorithms. Problem solving by computers is a central part of
the course.
Specifically
Knowledge and
understanding:
A successful student should
- be able to
discretize ordinary and partial differential equations and to independently
implement and to apply such algorithms.
Skills and
abilities:
A successful student should
- be able to independently select and apply computational algorithms.
- be able to evaluate both accuracy and relevance of numerical results.
- report solutions to problems and numerical results in written form
- on the construction of
basic mathematical models and algorithms.
- on the
numerical solution of a mathematical problem.
Course Outline
and Assignments |
|||||
Week |
Dates |
Sections |
Topic |
Assignment
(p) indicates programming |
|
1 |
1/18 |
Bits of ch.
1-2, Appendix A.1 9.4 |
Brief Intro
to Numerical Methods, ODE Review, Newton’s method for systems |
x2.1.3, x2.3.3,
x9.4.1, x9.4.4,
review
§2.2 and do exercises if you need to |
|
2 |
1/23, 1/25 |
3.1-3.3.3,
Matlab handout |
Explicit
Euler Method for IVPs Matlab
review and lab requirements |
x3.3.4,
x3.3.5, x3.3.7(p), x3.3.9 Lab 1, due
2/1 |
|
3 |
1/30, 2/1 |
3.3.4-3.5 |
Stiff
systems, Implicit Euler method and higher order methods |
x3.4.1,
x3.4.4(p), x3.4.6
Lab 2, due 2/18 |
|
4 |
2/6, 2/8 |
4.1-4.2.4 |
Finite
difference methods for Boundary Value Problems |
x4.2.3(p),
x4.2.4, x4.2.5 |
|
5 |
2/13, 2/15 |
Supplement,
4.2.5-4.3 |
Numerical
Methods for tridiagonal and sparse linear systems, nonlinear
BVP’s, shooting, “Ansatz methods” |
x4.2.8a(p),
x4.2.9(p),
additional
exercises
from linear algebra and §4.3 TBD |
|
6 |
2/20, 2/22 |
Ch 5 |
Monday: PDE
background
Wednesday: Exam I (Initial and Boundary-Value Problems, Linear
Algebra) |
Lab 3 due 2/29 |
|
7 |
2/27, 2/29 |
6.1-6.3 |
Parabolic
PDE via the method of lines |
x6.2.1(p),
x6.3.1, x6.3.3(p) |
|
8 |
3/5, 3/7 |
6.4-6.5 |
Nonlinear
parabolic PDE and ansatz methods |
Lab 4, due 3/21 |
|
3/12-3/16 Spring Break, no
classes.
L |
|||||
9 |
3/19, 3/21 |
7.1-7.3 |
Finite
Difference Method for Elliptic PDE |
x7.2.1, x7.2.2,
x7.3.1, x7.3.2 |
|
10 |
3/26, 3/28 |
7.4 |
Finite
Elements for Elliptic PDE |
Lab 5, due 4/11 |
|
11 |
4/2, 4/4 |
Supplementary materials |
Monday:
Parabolic and elliptic PDE advanced topics
Wednesday: Exam II (Parabolic and Elliptic Equations) |
Week 11-12 assignment,
due 4/18 |
|
12 |
4/9, 4/11 |
Supplementary materials |
Parabolic
and Elliptic PDE Advanced Topics |
||
13 |
4/16, 4/18 |
8.1-8.2 |
Finite
difference methods for Hyperbolic Problems |
x8.2.4,
x8.2.5(p), 8.2.6
|
|
14 |
4/23, 4/25 |
8.3 |
Numerical
Stability for Hyperbolic PDE |
Lab 6, due 4/30 |
|
15 |
4/30 |
Supplementary materials |
Advanced
Topics for Hyperbolic PDE |
||
IMPORTANT DATES |
|
FIRST DAY OF SEMESTER |
January 17 |
Exam I |
February 22 |
LAST DAY TO WITHDRAW |
March 20 |
Exam II |
April 4 |
LAST DAY OF CLASSES |
April 30 |
FINAL EXAM PERIOD |
May 3-9 |
Grading Policy
Assignment
Weighting |
|
Tentative
Grading Scale |
||
Exercises |
20% |
|
A |
90 -- 100 |
Computational Labs |
36% |
|
B+ |
85 -- 89 |
Midterm I |
12% |
|
B |
80 -- 84 |
Midterm II |
12% |
|
C+ |
75 – 79 |
Final Exam |
20% |
|
C |
65 – 74 |
|
|
D |
55 -- 64 |
|
|
F |
0 -- 54 |
Course Policies
Homework policy: Each week, a small number of exercises will be assigned, due
the following Wednesday at the beginning of class. In addition, parts of all
six “Computational Labs” from textbook appendix C will be assigned.
An average above 40% in each of the three areas (exercises, labs,
exams) is required to receive a passing grade, regardless of your overall
average.
Contacting me:
If a problem seems undoable or just plain wrong, then tell me or ask for my
help. Do not bang your head against a wall for a long time!
Attendance:
Mandatory
Cell phones:
This video explains my feelings. Also, if you try to hide your phone
under the desk while you text, I can see you!
Important Departmental and
University Policies
Prepared by Prof. Roy Goodman, January 12, 2012