MATH 332H Course Syllabus - spring 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 332-H02:  Honors Introduction to Functions of a Complex Variable

 

 

Instructor:  Prof. Bechtold 

Textbook:  Fundamentals of Complex Analysis, by E.B. Saff and A.D. Snider, 3rd Edition, Pearson Education, 2003, ISBN: 0-13-907874-6.

Prerequisites:  Grade of "B" or better in Math 222H or grade of "A" in Math 222.

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

Homework & Quizzes:

40%

Midterm Exam:

25%

Final Exam:

35%


NOTE:  This course needs to be passed with a grade of C or better in order to proceed to Math 495.

 


Drop Date:
 Please note that the University Drop Date March 20, 2012 deadline will be strictly enforced.

Homework Policy:  Homework problem sets will be assigned after each class based on the material covered, and will be due the following class. Late homework will not be accepted.

Quiz Policy:  A short quiz based on the homework problems will be given once each week.

Attendance:  Attendance at all classes will be recorded and is mandatory. Attendance record will determine 5% of the final grade, as specified in the grading policy above. More than 4 absences without a documented reason will result in the complete loss of this designated 4% component of the final grade.

Exams:  There will be one midterm exam during the semester and one comprehensive final exam during the final exam week at the end of the semester. The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the department's Examination Policy. This policy will be strictly enforced. Please note that calculators, cellular phones, beepers, and all other electronic devices may not be used nor turned on during any exam or quiz.

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.

January 16, 2012

M

Dr. Martin Luther King, Jr. Day ~ University Closed

March 11-18, 2012

Su-Su

Spring Recess ~ No Classes Scheduled ~ University Open

March 20, 2012

T

Last Day to Withdraw from this course

April 6, 2012

F

Good Friday ~ University Closed

May 1, 2012

T

Classes follow a Friday Schedule, Last Day of Classes

May 2, 2012

W

Reading Day

May 3-9, 2012

R-W

Final Exams


 

Course Outline and Homework Assignments:

 

Lecture

 Sections

Topics

Assignments

1

1.1-1.2

Algebra of Complex Numbers; Point/Vector Representation

pp. 4, 12

2

1.3-1.4

Polar Representation; Complex Exponential

pp. 22, 31

3

1.5

Powers and Roots

p. 37

4

1.6-1.7

Planar Sets; Stereographic Projection

pp. 43, 50

5

2.1-2.2

Functions of Complex Variable; Limits and Continuity

pp. 56, 63

6

2.3-2.4

Analyticity; The Cauchy-Riemann Equations

pp. 70, 77

7

2.5-2.6

Harmonic Functions; Steady-State Temperature

p. 84

8

3.1-3.2

Polynomials and Rational Functions; Exponential Function

p. 108

9

3.2-3.3

Trigonometric and Hyperbolic Functions; Logarithm

pp. 115, 123

10

3.4

Washers Wedges Walls

p. 129

11

3.5

Complex Powers; Inverse Trig

p. 136

12

4.1-4.2

Contours and Contour Integrals

pp. 159, 170

13

4.3-4.4

Independence of Path and Cauchy’s Integral Theorem

pp. 178, 199

14

4.5

Cauchy’s Integral Formula and its Consequences

p. 212

15

└►

REVIEW FOR Midterm Exam

 

16

└►

MIDTERM Examination

 

└►

SPRING RECESS:  MARCH 11-18, 2012

17

4.6

Bounds for Analytic Functions

p. 219

18

5.1-5.2

Sequences and Series; Taylor Series

pp. 239, 249

└►

(Mon. March 28) Last Day to Withdraw from this course

19

5.3

Power Series

p. 258

20

5.5

Laurent Series

p. 276

21

5.6-5.7

Zeros and Singularities; The Point at Infinity

pp. 285, 290

22

6.1

Residue Theorem

p. 313

23

6.2

Trigonometric Integrals over [0, 2π]

p. 317

24

6.3

Improper Integrals over (-∞ ; ∞)

p. 325

25

6.4

Improper Integrals involving Trigonometric Functions

p. 336

26

6.5

Indented Contours

p. 344

└►

GOOD FRIDAY ~ UNIVERSITY CLOSED

27

6.6

Integrals Involving Multiple-Valued Functions

p. 354

28

└►

REVIEW FOR FINAL EXAM

 STUDY FOR FINAL EXAM

└►

READING DAY (5/2)

 

Finals

Final EXAM WEEK:  May 3-9, 2012

 

Prepared By:  Prof. John Bechtold

Last revised:  December 7, 2011

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