MTH301 Fundamentals of Complex Analysis
Level: 3
Credit Units: 5 Credit Units
Presentation Pattern: EVERY JAN
Synopsis:
Complex numbers, complex functions and the analysis of functions of one complex varaible are
introduced. The understanding of the basic theory and the techniques of complex analysis is the ket to
succesful applications. The course aims to introduce the basic fundamental concepts and show how they
are woven together to provide a powerful tool for application.
Topics:
ƔComplex number field.
ƔComplex functions.
ƔSequences.
ƔSubsets of the complex plane.
ƔContinuous functions.
ƔLimits.
ƔComplex differentiation.
ƔPaths, rectifiable path, smooth path, length of a path.
ƔContour and contour integration.
ƔCauchy¶s integral theorem.
ƔCauchy¶s integral formula.
ƔTaylor and Laurent series, and residues.
Textbooks:
E.B. Saff and A.D, Snider: Fundamentals of Complex Analysis (PNIE-ISBN:9781292023755) 3rd
edition Pearson
ISBN-13: 9780130179685
E.B. Saff and A.D, Snider: Fundamentals of Complex Analysis (PNIE-ISBN:9781292023755) 3rd
edition Pearson
ISBN-13: 9780130179685-AA
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Learning Outcome:
ƔInterpret properties of complex numbers and complex valued functions.
ƔSolve convergence problems of complex valued sequences and series.
ƔEmploy limits, continuity of complex valued functions.
ƔTest the derivative of a complex valued function.
ƔCompute the integral of a complex valued function, and relate to various open and closed paths.
ƔIndicate the nature of singularities of complex functions.
ƔConstruct a range of mathematical techniques to solve a variety of complex valued analysis
problems.
ƔFormulate solutions to problems individually and/or as part of a group.
ƔAnalyze and solve a number of problem sets within strict deadlines.
Assessment Strategies:
Continuous Assessment Component
COMPUTER MARKED ASSIGNMENT
COMPUTER MARKED ASSIGNMENT
COMPUTER MARKED ASSIGNMENT
Sub-Total
Weightage (%)
10
10
10
30
Examinable Component
Written Exam
Sub-Total
Weightage (%)
70
70
Weightage Total
100
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