# Math 332-001: Introduction to Functions of a Complex VariableFall 2018 Course Syllabus

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.

## Course Information

Course Description: Functions of a complex variable: Cauchy-Riemann equations, Cauchy-Goursat theorem, integration, series, residues, poles, geometrical aspects. Emphasis on techniques. Effective From: Fall 2010.

Number of Credits: 3

Prerequisites: Math 211 or Math 213 and Math 222 all with a grade of C or better.

Course-Section and Instructors

Course-Section Instructor
Math 332-001 Professor C. Turc

Office Hours for All Math Instructors: Fall 2018 Office Hours and Emails

Required Textbook:

 Title Complex Variables and Applications Author Brown Edition 9th Publisher McGraw-Hill ISBN # 978-0073383170

University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 12, 2018. It will be strictly enforced.

## Course Goals

Course Objectives:

• Gain deep understanding of the relevance and broad importance of the theory of analytic functions.
• Learn the meaning of theorems describing important properties of analytic functions, and understand their corollaries.
• Learn the deep connection between the series representations and integration properties of analytic functions.
• Learn applications of the Cauchy Residue Theorem, in particular its use in calculating certain definite integrals.
• Learn how to apply the knowledge of analytic functions to problems in applied mathematics, science and engineering.

### Course Outcomes

• Students gain deeper knowledge of the theory of analytic functions of a complex variable, and its broad applicability.
• Students gain deeper understanding of common elementary transcendental functions through the knowledge of their properties in the complex plane.
• Students are prepared for further study in more advanced mathematics, science and engineering courses.
• Students can apply their knowledge of the theory of analytic functions to solve problems in applied mathematics, fluid dynamics, electrodynamics, and other areas of science and engineering.

Course Assessment: The assessment of objectives is achieved through homework assignments and quizzes, and the in-class midterm and final examinations.

## Policies

DMS Course Policies: 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.

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

 Homework and Quizzes 28% Attendance 2% Midterm Exam 34% Final Exam 36%

Your final letter grade will be based on the following tentative curve.

 A 87 - 100 C 62 - 67 B+ 81 - 86 D 55 - 61 B 75 - 80 F 0 - 54 C+ 68 - 74

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Homework and Quiz Policy: Homework problem sets will be emailed at the end of each week, and will be based on the material covered that week. Late homework will not be accepted. A short quiz based on the homework problems will be given about every other week, and will be announced at least one day in advance.

Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:

 Midterm Exam October 16, 2018 Final Exam Period December 15 - 21, 2018

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 Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: There will be No make-up QUIZZES OR EXAMS during the semester. In the event an exam is not taken under rare circumstances where the student has a legitimate reason for missing the exam, the student should contact the Dean of Students office and present written verifiable proof of the reason for missing the exam, e.g., a doctor’s note, police report, court notice, etc. clearly stating the date AND time of the mitigating problem. The student must also notify the Math Department Office/Instructor that the exam will be missed.

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Math Tutoring Center: Located in Cullimore, Room 214 (See: Fall 2018 Hours)

Further Assistance: For further questions, students should contact their instructor. All instructors have regular office hours during the week. These office hours are listed on the Math Department's webpage for Instructor Office Hours and Emails.

All students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. The Department of Mathematical Sciences takes these policies very seriously and enforces them strictly.

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Fall 2018 Academic Calendar, Registrar)

Date Day Event
September 4, 2018 T First Day of Classes
September 10, 2018 M Last Day to Add/Drop Classes
November 12, 2018 M Last Day to Withdraw
November 20, 2018 T Thursday Classes Meet
November 21, 2018 W Friday Classes Meet
November 22 - 25, 2018 R - Su Thanksgiving Recess
December 12, 2018 W Last Day of Classes
December 13 & 14, 2018 R & F Reading Days
December 15 - 21, 2018 Sa - F Final Exam Period

# Course Outline

Lecture Sections Topic
1 1-.5 Complex Algebra; Vectors & Moduli; Complex Conjugate
2 6-11 Polar Representation; Products & Powers in Exponential Form; Roots
3 12 Regions in the Complex Plane
4 13-14 Functions of Complex Variable; Mappings
5 15-18 Limits and Continuity
6 19-23 Derivatives & Analyticity; The Cauchy-Riemann Equations
7 24-26 Analyticity; Cauchy-Riemann Equations in Polar Coordinates
8 27-29 Harmonic Functions; Uniquely Determined Functions; Reflection Principle
9 30-36 The Exponential and Logarithm, The Power Function
10 37-39 Trigonometric and Hyperbolic Functions
11 40 Inverse Trigonometric & Inverse Hyperbolic Functions
12 Review for the Midterm Exam
13 Midterm Exam - OCTOBER 16, 2018
14 41-49 Contour Integrals; Fundamental Theorem of Calculus
15 50-54 The Cauchy-Goursat Theorem & The Cauchy Integral Formula
16 55-59 The Extensions of the Cauchy Integral Formula
17 60-65 Taylor Series; Power Series Convergence
18 66-68 Laurent Series
19 69-72 Uniform Convergence; Integration & Differentiation of Power Series
20 73 Series Multiplication, Division, Composition
21 74-76 Cauchy’s Residue Theorem
22 77-84 Zeros and Singularities; The Point at Infinity
23 85-87 Improper Integrals from Fourier Analysis
24 88 Improper Integrals Continued: Jordan’s Lemma
25 89-90 Integrals Involving Indented Contours
26 91 Integration along a Branch Cut
27 92 Definite Integrals Involving Sines and Cosines
28 Review for Final Exam

Updated by Professor C. Turc - 9/4/2018
Department of Mathematical Sciences Course Syllabus, Fall 2018