MATH 671 Course Syllabus - fall 2012

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

Prof. Miura

 

 

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.

September 3, 2012

M

Labor Day ~ No classes

November 6, 2012

T

Last Day to Withdraw from this course

November 20, 2012

T

Classes follow a Thursday Schedule

November 21, 2012

W

Classes follow a Friday Schedule

November 22-25, 2012

R-Su

Thanksgiving Recess

December 13, 2012

R

Reading Day

December  14-20, 2012

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

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