Last modified: 27 Feb 2018 15:20
Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on the foundations in Analysis I, and explores the notions of Riemann integrability, Cauchy sequences, sequences of functions, and power series.
The techniques of careful rigourous argument seen in Analysis I will be further developed. Such techniques will be applied to solve problems that would otherwise be inaccessible. As in Analysis I, the emphasis of this course is on valid mathematical proofs and correct reasoning.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
|Campus||Old Aberdeen||Sustained Study||No|
- Riemann integrability: Riemann sums, basic properties, the Fundamental Theorem of Calculus, improper integrals
- Cauchy sequences: Cauchy's characterisation of convergent sequences, Cauchy criterion for series, rearrangements of series
- Sequences of functions: pointwise convergence, uniform convergence, properties of limits of functions, Dini's Theorem, series of functions
- Power series: convergence, continuity, differentiability, integrability, Taylor series, manipulations of power series
This is the total time spent in lectures, tutorials and other class teaching.
1st attempt - 1 two-hour written examination (80%); in-course assessment (20%).
Resit – 1 two-hour written examination paper. Maximum of written exam (100%) or written exam (80%) with carried forward in-course assessment (20%).
Informal assessment of weekly homework through discussions in tutorials.
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.