This course introduces students to complex function theory and partial differential equations.
This course introduces students to basic concepts and methods in calculus. Topics covered include: functions, limits, derivatives, chain rule, rates of change, maxima and minima, integration, integration by substitution, partial derivatives, classification of stationary points, differential equations, and separable equations. These methods are applied to real-world problems in various fields such as economics, business, and finance—for example, in analysing marginal functions and modelling growth.
This course introduces students to fundamental theories and basic techniques in complex analysis. Topics covered include: analytic functions, Cauchy-Riemann equations, harmonic functions, reflection principle, elementary functions, entire functions, branches of logarithms, zeros and singularities, contour integrals, Cauchy- Goursat theorem, Cauchy integral formula, fundamental theorem of algebra, maximum modulus principle, Taylor series and Laurent series, residues and poles, Cauchy’s residue theorem, application of residues, argument principle, Rouche’s theorem.