MATH 332 Course Syllabus

NJIT HONOR CODE:  All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code 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 Honor Code, students are obligated to report any such activities to the Instructor.

 

Math 332-001:  Introduction to Complex Variables

FALL 2009

 

Instructor:   Prof. Victor Matveev   

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

Prerequisites:  Math 222 with a grade of C or better.

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

▪ Quizzes and Homework:

27 %

▪ Attendance:

5 %

▪ Midterm Exam:

30 %

▪ Final Exam:

38 %


Your final letter grade will be based on the following tentative curve. This curve may be adjusted slightly at the end of the semester. NOTE:  This course needs to be passed with a grade of C or better in order to proceed to Math 495.

A

87-100

C

60-66

B+

81-86

D

53-59

B

74-80

F

0-52

C+

67-73

 

 

 

Drop Date:  Please note that the Drop Date November 2, 2009 deadline will be strictly enforced.

Homework:  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 5% 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. Exams are held on the following days.

Midterm Exam:

October 23, 2009

Final Exam Week:

December 11-17, 2009


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 to Examination Policy. This policy will be strictly enforced. Please note that calculators, cellular phones, beepers, and all other electronic devices may not be used during any exam.

Makeup Exam Policy:    No make-up quizzes or EXAMS will be given.  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.

September 7, 2009

M

Labor Day Holiday ~ University Closed.

November 2, 2009

M

Last Day to Withdraw from this Course.

November 24, 2009

T

Classes Follow a Thursday Schedule.

November 25, 2009

W

Classes Follow a Friday Schedule.

November 26-29, 2009

R-Su

Thanksgiving Recess ~ University Closed.


 

Course Outline:

Week
Dates

Sec.

Topic

H/W page

1
8/31 – 9.4

1.1-1.2

1.3-1.4

Algebra of Complex Numbers; Point/Vector Representation

Polar Representation; Complex Exponential

p.4, p.12

p.22, p.31

2
9/11

1.5-1.6

Powers and Roots; Planar Sets

p.37, p.43

3
9/14 – 9/18

1.6-1.7

2.1-2.2

Planar Sets (continued); Stereographic Projection

Functions of Complex Variable; Limits and Continuity

p.43, p. 50

p.56, p.63

4
9/21 – 9/25

2.3-2.4

2.5-2.6

Analyticity; The Cauchy-Riemann Equations

Harmonic Functions; Steady-State Temperature

p.70, p. 77

p.84

5
9/28 – 10/2

3.1-3.2

3.2-3.3

Polynomials and Rational Functions; Exponential Function

Trigonometric and Hyperbolic Functions; Logarithm

p.108

pp.115, 123

6
10/5 – 10/9

3.4-3.5

4.1-4.2

Washers Wedges Walls; Complex Powers; Inverse Trig

Contours and Contour Integrals

pp.129, 136

pp.159, 170

7
10/12 – 10/16

4.3-4.4

4.5

Independence of Path and Cauchy’s Integral Theorem

Cauchy’s Integral Formula and its Consequences

pp.178,199

p.199

8
10/19 – 10/23

10/19

10/23

Review for the Midterm Exam

Midterm Examination

9
10/26 – 10/30

4.6

5.1

Bounds for Analytic Functions

Sequences and Series

pp.219

p. 239

November 2, 2009:  (M) Last Day to Withdraw from this Course.

10
11/2 – 11/6

5.2

5.3

Taylor Series

Power Series

p.249

p.258

11
11/9 – 11/13

5.5

5.6-5.7

Laurent Series

Zeros and Singularities; The Point at Infinity

p.276

pp.285, 290

12
11/16 – 11/20

6.1

6.2

Residue Theorem

Trigonometric Integrals over [0, 2π]

p.313

p.317

                       November 25, 2009:  (W) Classes Follow a Friday Schedule.

13
11/23 – 11/25

6.3

6.4

Improper Integrals over (-¥, ¥)

Improper Integrals involving Trigonometric Functions

p.325

p.336

14
11/30 – 12/4

6.5

6.6

Indented Contours

Integrals Involving Multiple-Valued Functions

p.344

p.354

15
12/7

                     Review for the Final Exam

Finals

Final EXAM Week:  (F-R)  December 11-17, 2009

Prepared By:  Prof. Victor Matveev

Last revised:  August 3, 2009