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 651: Methods of Applied Mathematics I
Prerequisites: Math 222 or departmental approval.
Course Description: A survey of mathematical methods for the solution of problems in the applied sciences and engineering. Topics include: ordinary differential equations and elementary partial differential equations. Fourier series, Fourier and Laplace transforms, and eigenfunction expansions.
Textbook: There is no specific text for this course. We will, however, be drawing from a number of sources throughout the semester, and students are expected to consult these references as necessary (or as directed by the instructor). The following texts have been placed on reserve in the library:
▪ "Advanced Mathematical Methods for Scientists and Engineers", by C. M. Bender and S. A. Orszag.
▪ "Advanced Engineering Mathematics", by E. Kreyszig.
▪ "Nonlinear Dynamics and Chaos", by S. H. Strogatz
▪
"Elementary Applied Partial Differential Equations", by
R. Haberman.
Website: web.njit.edu/~yyoung/M651_Fall2011.htm
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework: |
30% |
▪ Midterm Exam: |
30% |
▪ Final Exam: |
40% |
Your final letter grade will be based on the following tentative curve.
A |
90-100 |
C |
60-69 |
B+ |
85-89 |
D |
55-59 |
B |
80-84 |
F |
0-54 |
C+ |
70-79 |
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Drop Date: Please note that the University Drop Date November 3, 2011 deadline will be strictly enforced.
Homework Policy: Homework examples will be assigned every one to two weeks, with a clear due date. A substantial part of your grade is based on your ability to work these examples. Assignments will not be accepted past the due date.
MATLAB Assignments: Three MATLAB assignments will be given during the semester; tutors able to help students having difficulties are available in Cullimore 706 in accordance with a posted schedule.
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 Holiday ~ University Closed |
|
R |
Last Day to Withdraw from this course |
|
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline:
Lecture |
Dates |
Topics (See course website for assignments.) |
|
||
1 |
Sep 1 |
Linear ODE's. IVP's and BVP's. |
2 |
Sep 6 |
Basic existence and uniqueness results. |
3 |
Sep 8 |
Solution techniques for homogeneous equations. |
4 |
Sep 13 |
Solution techniques for homogeneous equations. |
5 |
Sep 15 |
Solution techniques for inhomogeneous equations. |
6 |
Sep 20 |
Solution techniques for inhomogeneous equations. |
7 |
Sep 22 |
Local analysis: Power series. |
8 |
Sep 27 |
Local analysis: Special functions. |
9 |
Sep 29 |
Special functions of mathematical physics. |
10 |
Oct 4 |
Special functions of mathematical physics. |
11 |
Oct 6 |
Nonlinear ODEs. Systems of first order equations, equilibrium points and their stability.
|
12 |
Oct 11 |
Nonlinear ODEs. Systems of first order equations, equilibrium points and their stability.
|
13 |
Oct 13 |
Calculus of variations: Introduction. |
14 |
Oct 18 |
Calculus of variations: Euler's differential equation for an extremal. |
15 |
Oct 20 |
Review of vector calculus. Grad, div, and curl. The use of suffix notation. |
16 |
Oct 25 |
Review of vector calculus. Grad, div, and curl. The use of suffix notation. |
17 |
Oct 27 |
The integral transformation theorems of vector calculus. Examples. |
18 |
Nov 1 |
The integral transformation theorems of vector calculus. Examples. |
19 |
Nov 3 |
Linear PDE's. Derivation of three classical equations of mathematical physics.
|
20 |
Nov 8 |
Linear PDE's. Derivation of three classical equations of mathematical physics.
|
21 |
Nov 10 |
Solution of BVP's and IBVP's by eigenfunction expansion. Method of characteristics. |
22 |
Nov 15 |
Solution of BVP's and IBVP's by eigenfunction expansion. Method of characteristics. |
23 |
Nov 17 |
Solution by integral transform techniques. Laplace transforms. |
24 |
Nov 22 |
Solution by integral transform techniques. Fourier transforms. |
25 |
Nov 24 |
Free-space Green's function: ODE. |
26 |
Dec 1 |
Free-space Green's function: PDE. |
27 |
Dec 3 |
Further applications of the Green's function. Additional topics and examples. |
28 |
Dec 8 |
Additional topics and examples (continued). |
|
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Finals |
Final EXAM WEEK: December 14-20, 2011 |
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Prepared By: Prof. Yuan N. Young
Last revised: August 22, 2011