On successful completion of this module, students will be able to:

apply the basic theory of convergence of sequences and series to
a range of examples;

calculate partial derivatives involving
algebraic and transcendental functions (including
trigonometric functions, exponential, logarithm, hyperbolic functions
and inverses);

apply the standard results and concepts concerning
differentiation in
a number of appropriate contexts (such as graphical or geometric
interpretations of tangents, critical points,
linear approximation,
solving simple linear differential equations);

compute double and triple integrals by application of Fubini's
theorem or use change of variables;

use integrals to find quantities defined
via integration in a number of context (such as average,
area, volume, mass).

Module Content

These details may be varied somewhat in the current year.

Sequences (definition and basic results on convergence).

Series (definition of the sum, seriese of positive terms, absolute convergence, tests for convergence).

Power series and (use of) Taylor's theorem.

Differentiation of curves, tangent lines in 2 or 3 dimensions.

Graphical representation of functions of 2 or 3 variables.

Patrial derivatives, gradients, direction derivatives, tangent planes to graphs and level surfaces.

Linear approximation for functions of 2 or 3 variables, chain rule.

Linear and exact differential equations.

Double and triple integrals, computation via iterated integrals (Fubini theorem).

Double integrals in polar coordinates.

Module Prerequisite

MA1123 (Analysis on the real line I),
MA1111 (Linear Algebra I)

Assessment Detail

Regular assignments and tutorial work.
In class exams twice in the term (at dates to be advised).
No annual examination.
For those requiring a supplemental examination, this will consist of 100% exam.