MA295 Real Analysis

• Continuity and differentiability of a function f:R^m->R^n, partial derivatives, directional derivatives, the Chain Rule
• Maxima and minima
• Revision of the main definitions and properties of sequences and series of real numbers
• Lim inf and lim sup, Cauchy's criterion for convergence, Taylor series, power series, uniform convergence, differentiation term by term
• Multiple integrals

Texts

• T.M. Apostol, "Mathematical Analysis" (Addison Wesley)

MA287 Complex Analysis

• Functions of a complex variable: differentiability, the Cauchy-Riemann equations, harmonic conjugates
• Line integrals, logz and e^z
• Cauchy's Integral Theorem, Cauchy's Formula, Cauchy's Inequalities
• The Laurent series of a function, poles, residues
• Contour integration, Rouché's Theorem
• Conformal mappings, Möbius transformations

Texts

• R.V. Churchill & J.W. Brown, "Complex Variables and Applications" (McGraw Hill)
• M.R. Spiegel, "Complex Variables" (Schaum Outline)

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