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Complex Calculus
Course Name 
Complex Calculus 
Course ID 
MCS21QCM 
Department 
Mathematics 
Subject 
Calculus 
Can you take this course more than once? 
No 
Periods per Day 
1.0 
Special Permission 
No 
Eligibility 
One of the following is true: All of the following are true:
 Student has passed AP Calculus Ab 1 Of 2 (MCS21X)
 One of the following is true:
 Student has passed AP Calculus Bc 2 Of 2 (MCS44X)
 Student is taking AP Calculus Ab 2 Of 2 (MCS22X)
 All of the following are true:
 Student has passed AP Calculus Bc 1 Of 2 (MCS43X)
 One of the following is true:
 Student has passed AP Calculus Bc 2 Of 2 (MCS44X)
 Student is taking AP Calculus Bc 2 Of 2 (MCS44X)
 All of the following are true:
 Student is taking Differential Equations (MCS66C)

Fulfills the following graduation requirements 

Also in the following groups 

Syllabus 
No Syllabus Found

Description
Complex Calculus is a yearlong elective course for advanced mathematics students, taught at the college level.
The aim of complex calculus is to investigate the ways in which ordinary calculus changes (or remains essentially the same) when we replace realvalued functions of a real variable with complexvalued functions of a complex variable. It turns out that there are many remarkable and unexpected differences. For example, in real calculus, a function can be once differentiable while failing to be twice differentiable. In complex calculus, a once differentiable function is automatically infinitely many times differentiable.
As part of the study of the complex plane, a good deal of topology will be covered; this is the study of continuous deformations of shape. Some highlights will include the Cauchy Integral Formula, the winding number and its applications to topology (such as the famous Brouwer Fixed Point Theorem), a rigorous proof of the Fundamental Theorem of Algebra, the calculus of residues, the CasoratiWeierstrass Theorem, and RouchÃ©'s Theorem (also known as the ""DogWalking Theorem""). ",Full year course