**School of Mathematics**

**
Module MA1132 - Advanced calculus
** 2011-12 (
JF Mathematics, JF Theoretical Physics & JF Two-subject
Moderatorship

SF Mathematics, SF Two-subject
Moderatorship
)

**Lecturer:** Professor Richard Timoney

**Requirements/prerequisites:** MA1123 (Analysis on the real line I),
MA1111 (Linear Algebra I)

**Duration:** Hilary term, 11 weeks

**Number of lectures per week:** 2 lectures and 1 tutorial per week

**Assessment:** Regular assignments and tutorial work.
In class exams Friday February 24 and (to be confirmed) Monday April
2nd.

**ECTS credits:** 5

**End-of-year Examination:**
Continuous assessment. Supplemental examination only.

**Description: **
Sequences (definition and basic results on convergence). Series
(definition of the sum, series 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.
Partial derivatives, gradients, directional 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.
Refer to `http://www.maths.tcd.ie/~richardt/MA1132` for more
information.

**Learning
Outcomes: **
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).

Apr 1, 2012

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