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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.
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