MTH 462 
Functions of Complex Variable
TuTh 2:00-3:15 PM
Tyler 109

Instructor    Araceli Bonifant  
Office: 202 G Lippitt Hall
Phone: 4-4394

Office Hours:

Textbook: Basic Complex Analysis
Jerrold E. Marsden and Michael J. Hoffman
W.H Freeman, ISBN: 0070109052

About the course: You will learn to work with complex numbers and functions of one complex variable.

At the end of the course you will be able to compute limits, derivatives, contour integrals and antiderivatives of functions of one complex variable. You will learn about the convergence of sequences and series.

You will learn important concepts and theorems such as: the definition of Cauchy-Riemann equations, the reflection principle, definition of harmonic functions, the exponential function, trigonometric functions, logarithmic functions, the Cauchy-Goursat theorem, the Cauchy integral formula, Liouville's theorem, Fundamental theorem of Algebra, Taylor series, Laurent series, absolute and uniform convergence of power series, residues theorems, residues at poles, zeros and poles of order m.

Time permitting you will be able to evaluate improper integrals and learn the Argument Principle and the Rouche's theorem.

Clicking here Course Schedule you will get a detailed syllabus of the course. The syllabus is always subject to change according to the needs of the class.

Prerequisites:  MTH 243 or equivalent.

Policies: You are expected to abide by the University's civility policy:

"The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."

Cell phones, IPods, beepers and any electronic device must be turned off in class.

You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.

Grading Policy:

Your grade will be determined by your scores on

  • Exam I                                     : 100pts
  • Exam II                                    : 100pts
  • Final                                         : 200pts    (cumulative)
  • Quizzes and Homeworks        : 100pts
  • Total                                        : 500pts
  • Homework: Homework will be assigned weekly but not collected or graded.  However the weekly quiz may be based on homework assignments.  If you do your weekly homework assignments you will have no problem with the exams.

    Quizzes: There will be weekly or biweekly quizzes.  The quiz will be given on Thursday.  I will drop the lowest quiz at the end of the term.

    There will be no make up quizzes or exams.

    Exam Schedule:

    Exam I :           Thursday October 17th.         
    Exam II :         Tuesday November 26th.          
    Final Exam:    December 12th, 11:30 AM - 2:30 PM  

    The Academic Enhancement Center:
    The work in this course can be difficult. You can seek help at the Academic Enhancement Center (AEC) in Roosevelt Hall. AEC tutors can answer questions, clarify concepts, check your understanding, and help you to study. You can make an appointment or walk in anytime Mon-Thur 9 AM to 9 PM, Fri 9 AM to 1 PM, Sun 4 PM - 8 PM. For a complete schedule go to, call (401) 874-2367, or stop by the fourth floor in Roosevelt Hall.

    Students with Disabilities:
    Any student with a documented disability is welcome to contact me early in the semester so that we may work out reasonable accommodations to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.