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 for more information.

Learning Outcomes: On successful completion of this module, students will be able to:
Apr 1, 2012

File translated from TEX by TTH, version 3.89.
On 1 Apr 2012, 17:12.