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 690: Advanced Applied Mathematics III: Partial Differential Equations
Number of Credits: 3
Course Description: A practical and theoretical treatment of initial- and boundary-value problems for partial differential equations: Green's functions, spectral theory, variational principles, transform methods, and allied numerical procedures. Examples will be drawn from applications in science and engineering.
Textbook: It may be useful to own a book for this course but it is not required. The texts below and a copy of the course lecture notes are on reserve at the library circulation desk.
Also Useful: Boundary Value Problems of Mathematical Physics, Volumes I and II. By Ivar Stakgold. SIAM Classics in Applied Mathematics vol 29. ISBN 0-89871-456-7.
Instructor: (for specific course-related information, follow the link below)
Math 690-001 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework: |
65% |
▪ Midterm Exam: |
10% |
▪ Final Exam: |
25% |
Drop Date: Please note that the University Drop Date November 6, 2012 deadline 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.
M |
Labor Day ~ No classes |
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T |
Last Day to Withdraw from this course |
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T |
Classes follow a Thursday Schedule |
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W |
Classes follow a Friday Schedule |
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R-Su |
Thanksgiving Recess |
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R |
Reading Day |
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F- R |
Final Exams |
Course Outline:
Weeks |
Sections |
Topic |
1-5 |
Kevorkian, chapter 1. Or Stakgold, sections 7.1 to 7.5. |
The diffusion
equation:
free-space Green’s function.
Solution on an infinite, semi-infinite, or
bounded domain in 1D via Green’s functions.
Comparison with solution by eigenfunction
expansion and Laplace transforms.
Solution in 2D and 3D.
Uniqueness results. |
6-10 |
Kevorkian, chapter 2. Or Stakgold, chapter 6 and
sections 7.12 to 7.15. |
The Laplace
and Poisson equations:
free-space Green’s function.
Free-space solution for distributions of
sources and dipoles.
Green’s formula and basic results for
harmonic functions.
Construction of Green’s functions and
solution for Dirichlet and Neumann problems.
Comparison with solution by eigenfunction
expansion.
Existence and uniqueness results.
The Helmholtz
equation.
The Green’s function.
Series representation.
Examples. |
11-14 |
Kevorkian, chapter 3. Or Stakgold, sections 7.6 to 7.11. |
The wave
equation.
D’Alembert’s solution.
Free-space Green’s function.
Solution on an infinite, semi-infinte, or
bounded domain in 1D via Green’s functions.
Comparison with solution by characteristics
or by Fourier transforms.
Solution in 3D.
Uniqueness results. |
Prepared By: Prof. Michael Booty
Last revised: May 17, 2012