Syllabus  MA294
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 CauchyRiemann
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)
Back to 2nd Year Syllabus