MATH 331: Introduction to Partial Differential EquationsFall 2015 Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciencestakes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means thatthere must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, orany form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students areobligated to report any such activities to the Instructor.

COURSE INFORMATION

Course Description: Partial differential equations in science and engineering. Topics include initial- andboundary-value problems for parabolic, hyperbolic, and elliptic second-order equations. Emphasis is placed onseparation of variables, special functions, transform methods, and numerical techniques. Effective From: Fall2010.

Number of Credits: 3

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

Course-Section and Instructors

Course-Section Instructor

Math 331-001 Professor P. Petropoulos

Required Textbook:

Title Applied Partial Differential Equations

Author Haberman

Edition 5th

Publisher Pearson

ISBN # 0-321797051

Notes Homework/Projects will be e-mailed. Weekly Quiz.

University-wide Withdrawal Date: Please note that the last day to withdraw with a W is November 2, 2015.It will be strictly enforced.

Course Objectives: Understand the derivation of the PDEs that model important physical phenomena; learn toclassify the different types of such PDEs, and how to choose an appropriate method for solving them in orderto determine qualitative/quantitative features of such solutions.

POLICIES

DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department ofMathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policiesvery seriously and enforces them strictly.

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

Homework 30%

Midterm Exam I 20%

Midterm Exam II 20%

Final Exam 30%

Your final letter grade will be based on the following tentative curve. NOTE: This course needs to be passedwith 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

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you readand fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Email Policy: It is important that you regularly check your NJIT email account for class assignments andannouncements from your instructor. Rutgers students must make sure that they can receive e-mails from theinstructor who employs the University-run e-mail system for addressing the whole class.

Homework and Quiz Policy:Homework problem sets will be assigned weekly and solutions will be sent afterthe due date. Late homework is not accepted. There will be a weekly quiz.

MATLAB Assignments: A few MATLAB assignments will be given during the semester; for help with MATLABsee the Instructor or MATLAB tutors available at PC Mall 38 in accordance with the posted schedule: Fall 2015Hours, TBA.

Exams: There will be two midterm exams held in class during the semester and one comprehensive finalexam. Exams are held on the following days:

Midterm Exam I October 9, 2015

Midterm Exam II November 13, 2015

Final Exam Week December 15 - 21, 2015

The final exam will test your knowledge of all the course material taught in the entire course. Make sure youread and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report their absence during a midterm or final exam, please review therequired steps under the DMS Examination Policy found here:

http://math.njit.edu/students/policies_exam.php

ADDITIONAL RESOURCES

Math Help Desk: Located in PC Mall 38 (See: Fall 2015 Hours, TBA)

Further Assistance: For further questions, students should contact their instructor. All instructors haveregular office hours during the week. These office hours are listed on the Math Department's webpage forInstructor Office Hours and Emails.

All students must familiarize themselves with and adhere to the Department of Mathematical Sciences CoursePolicies, in addition to official university-wide policies. The Department of Mathematical Sciences takes thesepolicies very seriously and enforces them strictly.

Accommodation of Disabilities: NJIT is committed to providing students with documented disabilities equalaccess to programs and activities. If you have, or believe that you may have, a physical, medical,psychological, or learning disability that may require accommodations, please contact the Coordinator ofStudent Disability Services located in the Center for Counseling and Psychological Services, in Campbell Hall,Room 205, (973) 596-3414. Further information on disability services related to the self-identification,documentation and accommodation processes can be found on the webpage at:

http://www.njit.edu/counseling/services/disabilities.php

Important Dates (See: Fall 2015 Academic Calendar, Registrar)

Date Day Event

September 1, 2015 T First Day of Classes

September 7, 2015 M Labor Day - University Closed

September 8, 2015 T Monday Classes Meet

September 8, 2015 T Last Day to Add/Drop Classes

November 2, 2015 M Last Day to Withdraw

November 25, 2015 W Friday Classes Meet

November 26 - 29, 2015 R - Su Thanksgiving Recess - University Closed

December 10, 2015 R Last Day of Classes

December 11 & 14, 2015 F & M Reading Days

December 15 - 21, 2015 T - M Final Exam Period

Course Outline

WeekDate Lecture Sections Topic

9/1 1 1.2 General introduction to PDEs, Derivation of the Heat Equation in one spatialdimension

2 1.3+1.4 Boundary Conditions. Equilibrium Temperature Distribution

1.5 +Appendixto 1.5

Derivation of the Heat Equation in Higher Dimensions. This material will beassigned as a "reading." Students should review Calculus (Thomas textbook)sections 16.7-16.8

9/7 3 2.1 - 2.3 Method of Separation of Variables, the Heat Equation. Students should reviewOrdinary Differential Equations (Boyce & DiPrima textbook) sections 10.1-10.2,

10.4

9/14 4 2.4 Worked Examples with the Heat Equation

5 2.5 Laplace’s Equation, Solution by Separation of Variables

9/21 6 4.1 - 4.3 Derivation of the Wave Equation in 1D, the Vibrating String

7 4.4 - 4.6 Solution by Separation of Variables for the Vibrating String, Vibrating Membranes,Electromagnetic and Acoustic Waves

9/28 8 FromHandoutNotes

Classification of Partial Differential Equations. Further Examples of PartialDifferential Equation Models in Physics/Engineering.

9 12.1 -12.3

The Method of Characteristics for the Wave Equation

10/5 10 5.1 - 5.2,3.1-3.5

Sturm-Liouville Eigenvalue Problems: Introduction and examples. Fourier Series(review and a few new topics)

11 FRIDAY, 10/9, MIDTERM EXAM I ON CHAPTERS 1-2, 4

10/12 12 5.3 Sturm-Liouville Eigenvalue Problems: Classification and Theorems

13 5.4 Worked example: Heat flow in nonuniform rod

10/19 14 5.5 Self-Adjoint Operators and Sturm-Liouville Eigenvalue Problems

15 5.6 The Rayleigh Quotient

10/26 16 5.7 Example: Vibration of a Nonuniform String

17 5.8 Mixed Boundary Conditions

11/2 18 7.1 - 7.3 PDE Examples in 2D and 3D, Vibrations of a Rectangular Membrane

19 7.4 - 7.6 Statements and Theorems about Vibrating Linear Membranes

11/9 20 7.7 Vibrating Circular Membrane and Bessel Functions

21 FRIDAY, 11/13, MIDTERM EXAM II ON CHAPTER 5

11/16 22 8.2 - 8.3 Heat Flow with Sources and Nonhomogeneous Boundary Conditions

23 8.3 - 8.4 Eigenfunction Expansion for Nonhomogeneous Problems

11/23 24 10.2 -10.3

Heat Equation on an Infinite Domain. The Fourier Transform Pair

25 10.4 -10.5

Fourier Transform and the Heat Equation. The Heat Equation on Semi-infiniteIntervals

THANKSGIVING

11/30 26 10.6 Fourier Transform Solution of the Heat, Wave, and Laplace's Equations on Infiniteand Semi-infinite Intervals/Domains

27 10.6 Fourier Transform Solution of the Heat, Wave, and Laplace's Equations on Infiniteand Semi-infinite Intervals/Domains (Continued)

12/7 28 REVIEW FOR FINAL EXAM

Updated by Professor P. Petropoulos - 8/31/2015