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
2013 Course Syllabus:
Math 440
|
Course Title: |
Advanced Applied
Numerical Methods |
| Instructor: |
Peter
G. Petropoulos, Phone: 973-596-5626,
E-mail: peterp@njit.edu, Office Hours:
TBA |
|
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 textbook) |
|
Prerequisites: |
Math 331
(Introduction to Partial Differential
Equations
), Math 340 (
Applied Numerical
Methods) |
Note: This
webpage will not be updated. An additional webpage
with homework and computational lab assignments,
selected solutions, up-to-date guidelines, and
additional lecture-related information is located
here.
Course Objectives:
The
aim of the course is to teach computational methods
for solving ordinary and partial differential
equations that arise in scientific problems. This
includes the construction, analysis, and application
of basic computational algorithms.
Specifically
Knowledge and understanding:
A successful student should
- be able to discretize ordinary and
partial differential equations and to independently
implement, verify, and apply the resulting 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.
- be able to report solutions to problems and numerical results in written form.
|
Course
Outline and Assignments |
||
|
Week |
Sections |
Topic |
|
1 |
Chapters 1-2,
Appendix A.1, Section 9.4 |
Introduction to
course, ODE and Initial Value Problems
(IVP's) review, Newton’s method for
nonlinear algebraic systems,
nondimensionalization |
|
2 |
Sections 3.1-3.3.3 |
Explicit Euler
Method for IVPs, Matlab review |
|
3 |
Sections 3.3.4-3.5 |
Stiffness, implicit
Euler method, and higher order methods |
|
4 |
Sections 4.1-4.2.4 |
Finite difference
methods for Boundary Value Problems (BVP's) |
|
5 |
Sections 4.2.5-4.3 |
Numerical Methods
for tridiagonal and sparse linear systems,
nonlinear BVP’s, shooting, “Ansatz methods” |
|
6 |
Chapter 5 |
Tuesday, 2/26:
Review of PDE's Friday,
3/1: Exam I on what was covered in Weeks 1-5 |
|
7 |
Sections 6.1-6.3 |
Parabolic PDE's via
the method of lines |
|
8 |
Sections 6.4-6.5 |
Nonlinear parabolic
PDE's and "Ansatz methods" |
|
3/17-3/24 Spring
Break, no classes. |
||
|
9 |
Sections 7.1-7.3 |
Finite Difference
Method for Elliptic PDE's |
|
10 |
Section 7.4 |
Finite Elements for
Elliptic PDE's |
|
11 |
Supplementary
materials |
Tuesday, 4/9:
Parabolic and elliptic PDE advanced topics Friday,
4/12: Exam II on what was covered in Weeks
6-10 |
|
12 |
Supplementary
materials |
Parabolic and
Elliptic PDE's Advanced Topics |
|
13 |
Sections 8.1-8.2 |
Finite difference
methods for Hyperbolic Problems |
|
14 |
Section 8.3 and
Supplementary material |
Numerical Stability
for Hyperbolic PDE's, the effect of boundary
conditions, phase error |
|
IMPORTANT
DATES |
|
|
FIRST
DAY OF SEMESTER |
January
22 |
|
Exam
I |
March
1 |
|
LAST
DAY TO WITHDRAW |
March
26 |
|
Exam
II |
April
12 |
|
LAST
DAY OF CLASSES |
May
7 (Friday schedule) |
|
FINAL
EXAM PERIOD |
May
9-15 |
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 Tuesday at the beginning of class.
In addition, parts of all six “Computational Labs”
from textbook appendix C will be assigned.
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. Peter G. Petropoulos, January 4, 2013