University:

Email Address:

Phone Number:

Complex Variable University of Galway - Engineering & Computer Science Program Spring 2022 Semester - Galway

Flight Credit Get a Flight Credit worth up to $350 when you apply with code* by May 6, 2024

Complex Variable

Complex Variable Course Overview

OVERVIEW

CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA302
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 2.5
Contact Hours: 36

DESCRIPTION

This course introduces complex variable theory. Topics covered include: Cauchy-Riemann equations, Laplace's equation, complex numbers to the power of complex numbers, Integral evaluation in the complex plane, Cauchy's integral theorem, Cauchy's integral formula and Cauchy's integral formulae for derivatives, residues and the residue theorem.

Learning Outcomes
1. Simplify complex numbers and plot the result in the Argand diagram. Calculate derivatives of a complex function. Define: complex conjugate, real part and imaginary part of a complex number.
2. Use the Cauchy-Riemann equations to find the points in the complex plane where a function is differentiable. Compute the derivative at these points.
3. Show that certain functions are harmonic functions and calculate the harmonic conjugate of a harmonic function.
4. Write complex numbers in polar form; find and plot their roots in the complex plane. Find complex powers of complex numbers and write the result in polar form or in the form: a+ib. Verify expressions for various inverse trigonometrical functions.
5. State Cauchy's integral theorem and all the associated technical details. Compute integrals of analytic and non-analytic functions over various paths in the complex plane.
6. State Cauchy's integral formula and Cauchy's integral formula for derivatives. Use these to compute integrals around simple closed curves where there are poles within these simple closed curves.
7. Obtain the Taylor series centered about a point. Find the Laurent series centered about a point valid in different regions.
8. State the Residue Theorem. Use it to compute integrals around simple closed curves.

Receive a $350 Flight Credit when you apply by May 06, 2024

Get your flight credit code and access to Passbook in two easy steps. With Passbook, you can track your favorite programs and courses, save flight credits, and watch videos on the destination you're interested in.

Apply Now

Step 1 of 2

Step 2 of 2


*By providing your mobile number, you agree to receive recurring text messages from CEA CAPA Education Abroad notifying you of important program deadlines. Message and data rates may apply.

Privacy Policy   |   Mobile Terms   |   Flight Credit Rules

Your flight credit has been added to your Passbook. Apply now or view your Passbook to begin the next step in your journey.

Speak with an
Admissions Advisor

Schedule an appointment to speak with a study abroad expert.

Book Appointment
LET'S CHAT