CIS Abroad has joined forces with
CEA CAPA Education Abroad
As part of the CEA CAPA Education Abroad family, you'll find even more opportunities with our expanding global network.
Barcelona SAE has joined forces with
CEA CAPA Education Abroad
As part of the CEA CAPA Education Abroad family, you'll find even more opportunities with our expanding global network.
Complex Analysis
University of Galway - Direct Enroll Program
Galway, Ireland
Dates: early Jan 2028 - early May 2028
Complex Analysis
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA2287
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
This module introduces the theory of functions of a complex variable, statring with an introduction to complex numbers and ending with applications of the Residue Theorem and conformal transformations.
Learning Outcomes
1. represent a complex number as a point in the plane; calculate the modulus and argument of a complex number; switch between cartesian and polar forms; calculate the n-th roots of a complex number
2. decide where a function is diffrentiable (resp. analytic) using the Cauchy-Riemann equations
3. calculate the complex derivative of a function; decide whether a function is harmonic; calculate the harmonic conjugate of a harmonic function;
4. do various calculations involving exponentials and logarithms
5. parameterize a variety of paths in the plane
6. calculate the integral of a function along a given path
7. apply Cauchy's Theorem to compute integrals; apply Cauchy's Integral Formula to calculate various integrals;
8. calculate the Taylor series of a variety of elementary functions;
9. deduce the Laurent series of a range of functions;
10. apply the Residues Theorem to calculate various improper integrals.
Learning Outcomes
1. represent a complex number as a point in the plane; calculate the modulus and argument of a complex number; switch between cartesian and polar forms; calculate the n-th roots of a complex number
2. decide where a function is diffrentiable (resp. analytic) using the Cauchy-Riemann equations
3. calculate the complex derivative of a function; decide whether a function is harmonic; calculate the harmonic conjugate of a harmonic function;
4. do various calculations involving exponentials and logarithms
5. parameterize a variety of paths in the plane
6. calculate the integral of a function along a given path
7. apply Cauchy's Theorem to compute integrals; apply Cauchy's Integral Formula to calculate various integrals;
8. calculate the Taylor series of a variety of elementary functions;
9. deduce the Laurent series of a range of functions;
10. apply the Residues Theorem to calculate various improper integrals.