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Basic Details:

  • Course Code: EM 5050
  • Credits: 3
  • Pre-requisites: EM 2010
  • Compulsory/Optional: Optional

Aim :

To provide a thorough knowledge of fundamental and advanced concepts in complex analysis for applications.

Intended Learning Outcomes:

At the end of the course, students should be able to;

  • Evaluate contour integrals by use of Cauchy’s Integral theorems.
  • Represent complex functions in Taylor and Laurent Series and identify domains of convergence.
  • Classify singularities of a complex function.
  • Evaluate real integrals using residue calculus and apply these methods in finding integral transforms such as Inverse Laplace, Fourier and Hilbert transforms.
  • Apply the Argument Principle and Roche’s theorem to locate roots of polynomial equations.
  • To construct simple conformal mappings and apply conformal mapping to solve
    problems from engineering.

Couse Content:

Convergence, Tests for convergence, Power series, Taylor series, Laurent series

Singularities and classification, Residue theorem, Calculation of residues.

Trigonometric, improper Integrals, poles on the real line, principal values, integration on branch cuts.

Applications to integral transforms (Fourier, Laplace and Hilbert transforms)

Argument principle, Rouche’s theorem, and stability of systems.

Complex mapping functions, Riemann's mapping theorem, general transformations, linear transformation, bilinear transformation, selected special transformations, inverse transformations, Schwarz-Christoffel transformation and applications.

Time Allocation (Hours):

Lectures
0
Assignments
0

Recommended Texts:

  •  E.B. Staff and A.D. Snider, “Fundamentals of Complex Analysis with applications to engineering and science”, Pearson 3rd edition.
  • Elias Stein & Rami Shakarchi, “Complex Analysis” (2003), Princeton (2003).
  • R.V. Churchill & J.W. Brown, “Complex variables and applications”, 9th edition, McGraw-Hill.

Assessment:

In - course:

Tutorials/Quizzes
20%
Mid Semester Examination
30%

End-semester:

50%