NJIT HONOR CODE

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

Link to Solutions

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

Homework 8

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

Homework 10

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

Week 14 assignment

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