Last modified: 23 Aug 2017 15:27
Analysis provides the rigourous, foundational underpinnings of calculus. It is centred around the notion of limits: convergence within the real numbers. Related ideas, such as infinite sums (a.k.a. series), continuity, and differentiation, are also visited in this course.
Care is needed to properly use the delicate formal concept of limits. At the same time, limits are often intuitive, and we aim to reconcile this intuition with correct mathematical reasoning. The emphasis throughout this course is on rigourous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.
Study Type  Undergraduate  Level  2 

Session  First Sub Session  Credit Points  15 credits (7.5 ECTS credits) 
Campus  Old Aberdeen  Sustained Study  No 
Coordinators 

 Fundamental properties of real numbers: field operations, order, completeness.
 Sequences and limits: convergence, basic examples, methods of deducing convergence, properties of convergent sequences, the BolzanoWeierstrass Theorem.
 Infinite sums (series): convergence, convergence tests.
 Functions of one real variable: limits and continuity, methods of deducing limits, Extreme Value Theorem, Intermediate Value Theorem, uniform continuity.
 Differentiation of functions of one variable: basic definitions and properties, chain rule, basic results on differentiable functions, Rolle's Theorem, Mean Value Theorem.
Syllabus
This is the total time spent in lectures, tutorials and other class teaching.
Informal assessment of weekly homework through discussions in tutorials.
We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.