MATH 331 Course Syllabus - SPRING 2012

NJIT Academic Integrity CODE:  All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly.  This means that 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 University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

 

Math 331:  Introduction to Partial Differential Equations

 

Number of Credits:  3

 

Course Description:  Partial differential equations in science and engineering. Topics include initial- and boundary-value problems for parabolic, hyperbolic, and elliptic second-order equations. Emphasis is placed on separation of variables, special functions, transform methods, and numerical techniques. Effective From: Fall 2010

 

Prerequisites:  Math 211 or Math 213 and Math 222 with a grade of C or better.

Textbook:  Applied Partial Differential Equations by Richard Haberman (4th Ed); Pearson Prentice-Hall, ISBN: 0130652431. 

Instructor:   (for specific course-related information, follow the link below)

 

Math 331-002

Prof. Boubendir

Math 331-004

Prof. Ratnaswamy

 

Grading Policy:  The final grade in this course will be determined as follows: 

Homework & Quiz:

35%

Midterm Exam:

30%

Final Exam:

35%


Your final letter grade will be based on the following tentative curve. NOTE:  This course needs to be passed with a grade of C or better in order to proceed to Math 440, Math 450H, Math 475, and Math 495.

A

88-100

C

60-66

B+

81-87

D

54-59

B

74-80

F

0-53

C+

67-73

 

 

 

Drop Date:  Please note that the University Drop Date March 20, 2012 deadline will be strictly enforced.

Email:  It is important that you regularly check your NJIT email account for class assignments and announcements from your instructor. Rutgers students should email the Instructor their preferred email address at the start of the semester.

Homework and Quizzes:  Homework assignments listed in the syllabus are tentative. Homework problem sets will be emailed by the instructor after each class. Homework is due on the assigned date; late homework is not accepted. Quizzes are given about once per week on an announced topic.

MATLAB Assignments:  Three MATLAB assignments will be given during the semester; for help with MATLAB see the Instructor or MATLAB tutors available in accordance with the posted schedule.

Attendance and Participation:  Attendance in this class is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.

Makeup Exam Policy:  There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.

Further Assistance:  For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.


 

MATH DEPARTMENT CLASS POLICIES LINK 

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

January 16, 2012

M

Dr. Martin Luther King, Jr. Day ~ University Closed

March 11-18, 2012

Su-Su

Spring Recess ~ No Classes Scheduled ~ University Open

March 20, 2012

T

Last Day to Withdraw from this course

April 6, 2012

F

Good Friday ~ University Closed

May 1, 2012

T

Classes follow a Friday Schedule, Last Day of Classes

May 2, 2012

W

Reading Day

May 3-9, 2012

R-W

Final Exams


 

Course Outline And Homework Assignments:

 

Week
Dates

Lecture, Section & Topic

Assignments

Week 1

1

3.1-3.3

Intro to PDEs; Review: ODEs, Calculus III, Fourier Series

Assigned in class

2

3.4-3.6

Fourier Series; Term-by-term Operations

Assigned in class

Week 2

 

 

3

1.2

Heat Equation: 1D Derivation

S1.2: 3,5,9

Week 3

4

1.3

Heat Equation: Boundary Conditions

S1.3: 1,2

5

1.4

Heat Equation: Equilibrium temperature Distribution

S1.4: 1, 3, 7, 10, 11

Week 4

6

1.5

Heat Equation: Higher Dimensions

S1.5: 5,9,10,11,12,13

7

2.1-2.3

Heat Equation: 1D Solution I

S2.2: 2;

S2.3: 1, 2, 3, 8,

Week 5

8

2.4

Heat Equation: 1D Solution II

S2.4: 1, 3, 4

9

2.5

Laplace’s Equation: Solution

S2.5: 1, 3, 5(b,c), 7, 8(b),15(a,c)

Week 6

10

4.1-4.3

Wave Equation: 1D Derivation

S4.2: 1; S4.3: 1, 2

11

4.4

Wave Equation: Vibrating String

S4.4: 1, 2, 3, 5

Week 7

12

└►

REVIEW FOR EXAM #1

STUDY FOR EXAM #1

13

└►

MIDTERM EXAM I:

Week 8

14

5.1-5.3

Sturm-Liouville Problems

S5.3: 4, 8, 9

15

5.4

Sturm-Liouville Problem : Heat Flow in Nonuniform Rod

S5.4: 1, 2, 3

Week 9

16

5.5

Sturm-Liouville Problems: Self-Adjointness

S5.5: 1(d), 8, 9

17

5.6

Sturm-Liouville Problems: Rayleigh Quotient

S5.6: 1, 2

Week 10

└►

Last Day to Withdraw(3/20) from this course

18

5.7

Sturm-Liouville Problems: Application to Wave Equation

S5.7: 1

19

5.8

Sturm-Liouville Problems: Mixed Boundary Conditions

S5.8: 5, 6, 7

Week 11

20

6.1-6.3

Finite Difference Numerical Methods for PDEs

S6.2: 1,2,3,4; S6.3:1

21

7.1-7.3

PDE’s in 2D: Vibration of a Rectangular Membrane

S7.3: 1, 3, 4

Week 12

22

7.7

Vibration of a Circular Membrane

S7.7: 4, 9, 10

23

7.8

More on Bessel Functions

S7.8: 5, 8

Week 13

24

8.1-8.2

Heat Flow with Non-homogeneous Boundary Conditions

Assigned in class

25

8.3

Nonhomogeneous Problems: Eigenfunction Expansion

S8.3: 6

Week 14

26

9.1-9.2

Green’s Functions: 1D Heat Equation

Assigned in class

27

9.3

Green’s Functions: BVP’s for ODE’s

Assigned in class

Week 15

28

└►

REVIEW FOR FINAL EXAM

STUDY FOR FINAL EXAM

 

Finals

Final EXAM WEEK: may 3-9, 2012

Prepared By:  Prof. Yassine Boubendir

Last revised:  December 9, 2011

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