Syllabus  MA201
MA211 Calculus (part one)

Methods of integration: substitution, integration by parts, partial fractions,
reduction formulae

Inverse functions

Improper integrals (as limits of finite integrals)

Differential equations: linear equations with constant coefficients, first
order homogeneous equations.
MA212 Calculus (part two)

Series: convergence, divergence, absolute convergence

The Comparison, Integral and Ratio Tests

Alternating series

Power series, the Radius of convergence

Functions of several variables, and vectorvalued functions (in R^{2}
and R^{3}): vectors, scalar product, cross product in R^{3},
equations of lines and planes in parametric form

Partial derivatives: gradients, tangent planes, maxima and minima of functions
of 2 variables, Lagrange multipliers

The Chain Rule
Texts

G.B. Thomas & R.I. Finney, "Calculus and Analytic Geometry" (Addsison
Wesley)

S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables"
(Wiley)
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