MATH 722 Course Syllabus

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 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 Honor Code, students are obligated to report any such activities to the Instructor.

 

Math 722-001:  Wave Propagation

FALL 2009

 

Instructor:  Prof. Moore 

Textbook:  There is no prescribed text, but listed below are a number of books that have been put on reserve in the library. Much of the course material will be drawn from the first reference by Whitham.

        G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, 1999, ISBN 0-471-35942-4.

        R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press, 1997, ISBN 0-521-59172-4.

        J. L. Davis, Mathematics of Wave Propagation, Princeton University Press, 2000, ISBN 0-691-02643-2.

        D. F. Parker, Fields, Flows and Waves, Springer, 2003, ISBN 1-85233-708-7.

        J. Billingham & A. C. King, Wave Motion, Cambridge University Press, 2000, ISBN 0-521-63450-4.

       C. A. Coulson & A. Jeffrey, Waves: A Mathematical Approach to the Common Types of Wave Motion, Longman, 1977, ISBN 0-582-44954-5.

        J. L. Davis, Mathematics of Wave Propagation, Princeton University Press, 2000, ISBN 0-691-02643-2.

        D. F. Parker, Fields, Flows and Waves, Springer, 2003, ISBN 1-85233-708-7.

        J. Billingham & A. C. King, Wave Motion, Cambridge University Press, 2000, ISBN 0-521-63450-4.

       C. A. Coulson & A. Jeffrey, Waves: A Mathematical Approach to the Common Types of Wave Motion, Longman, 1977, ISBN 0-582-44954-5.

Prerequisites:  Departmental approval. Students will be expected to be familiar with classification of partial differential equations, integration in the complex plane, and transform techniques.

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

Homework:

40%

Midterm Exam:

25%

Final Exam:

35%

 

Drop Date:  Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced.

Homework:  An assignment will be handed out and collected in class roughly every two weeks. Communication relevant to the course, including assignment postings, will be done through the course site on Highlander Pipeline.

Exams:  There will be one midterm exam during the semester and one comprehensive final exam during the final exam period.

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.

September 7, 2009

M

Labor Day Holiday ~ University Closed

November 2, 2009

M

Last Day to Withdraw from this course

November 24, 2009

T

Classes follow a Thursday Schedule

November 25, 2009

W

Classes follow a Friday Schedule

November 26-29, 2009

R-Su

Thanksgiving Recess ~ University Closed


 

Course Outline:

Course material will include (a subset of) the following topics:

 

  

Hyperbolic Waves, Characteristics, Riemann Invariants

Shocks, Weak Solutions, Rankine-Hugoniot Conditions

Dispersive Waves, Wave Packets, Precursors

Gas Dynamics, Water Waves, Elastic Waves, Electromagnetic Waves

Reduced Wave Models: Burgers, Klein-Gordon, Nonlinear Schrödinger, Etc.

Asymptotic Methods (WKBJ, Geometrical Optics, Stationary Phase, Steepest Descent)

Solitons and Exactly Integrable Systems

Linear & Nonlinear Stability

Variational Methods, Whitham’s Modulation Theory

Ship Waves

Geometric Methods for Traveling Waves

Waves in Periodic or Disordered Media, Invariant Imbedding

Waves in Layered or Anisotropic Media (Elasticity, Crystal Optics)

  

FINAL EXAM Week:  December 11-17, 2009

   

 

 

Course Notes:

 

Week 1
8/31 – 9/4

Week 2
9/7 – 9/11

Week 3
9/14 – 9/18

Week 4
9/21 – 9/25

Week 5
9/28 – 10/2 

Week 6
10/5 – 10/9

Week 7
10/12 – 10/16

Week 8
10/19 – 10/23

Week 9
10/26 – 10/30

Week 10
11/2 – 11/6

Week 11
11/9 – 11/13

Week 12
11/16 – 11/20

Week 13
11/23 – 11/27

Week 14
11/30 – 12/4

Week 15
12/7 – 12/9

Finals Week
12/11 – 12/17

 

Prepared By:  Prof. Richard Moore

Last revised:  August 3, 2009

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