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 671: Asymptotic Methods I
Number of Credits: 3
Course Description: Asymptotic sequences and series. Use of asymptotic series. Regular and singular perturbation methods. Asymptotic methods for the solution of ODEs, including: boundary layer methods and asymptotic matching, multiple scales, the method of averaging, and simple WKB theory. Asymptotic expansion of integrals, including: Watson's lemma, stationary phase, Laplace's method, and the method of steepest descent.
Prerequisites: Math 645 or Math 545, and Math 656 or departmental approval.
Textbook: J.D. Murray, Asymptotic Analysis, Springer-Verlag, New York, 1984, ISBN-13: 978-0387909370.
Instructor: (for specific course-related information, follow the link below)
Math 671-001 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Hand-in Homework: |
25% |
▪ Midterm Examinations: |
35% |
▪ Final Examination: |
40% |
Your final letter grade will be based on the following tentative curve.
A |
90-100 |
C |
60-74 |
B+ |
85-89 |
D |
55-59 |
B |
80-84 |
F |
0-54 |
C+ |
75-79 |
|
|
Drop Date: Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.
Homework Policy: There will be hand-in homework.
Attendance:
Attendance in all classes is strongly encouraged.
Absences from class will
inhibit your ability to learn and will affect your grade.
Late arrival to class is very disruptive and will not be
tolerated.
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 electronic devices (cellular phones, beepers, iPods, laptops, etc.) must be switched off during all class and exam 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 |
|
T |
Last Day to Withdraw from this course |
|
T |
Classes follow a Thursday Schedule |
|
W |
Classes follow a Friday Schedule |
|
R-Su |
Thanksgiving Recess |
|
R |
Reading Day |
|
F- R |
Final Exams |
Course Outline:
Week |
Sections |
Topic |
1 |
1.1 |
Introduction, Concepts, and Notation |
2 |
1.2 |
Asymptotic Sequences, Expansions, and Series
Asymptotology, Polynomial Equations |
3 |
2.1
|
Asymptotic Evaluation of Integrals
Integration by Parts, Watson’s Lemma |
4 |
2.2 |
Laplace’s Method
Gamma Function |
5 |
3.1 |
Method of Steepest Descent
Saddle Point Method |
6 |
3.2 |
Examples |
7 |
4.1 |
Method of Stationary Phase
Applications |
8 |
5.1 |
Fourier Transforms
Laplace Transforms |
9 |
|
MIDTERM |
10 |
6.1 |
Differential Equations – Singularities
Asymptotic Methods of Solution |
11 |
6.2 |
Special Functions
WKB Method – Liouville Equation |
12 |
6.3 |
Examples
Turning Point Problems – Airy Equation |
13 |
7.1 |
Singular Perturbation Problems
Boundary Layers |
14 |
7.2 |
Method of Matched Asymptotic Expansions
Method of Multiple Scales |
15 |
|
Secular Terms
Review |
Prepared By: Prof. Robert Miura
Last revised: August 4, 2012