Last modified: 25 May 2018 11:16
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.
Study Type  Undergraduate  Level  2 

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

 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
Syllabus
This is the total time spent in lectures, tutorials and other class teaching.
1^{st} attempt  1 twohour written examination (80%); incourse assessment (20%).
Resit – 1 twohour written examination paper. Maximum of written exam (100%) or written exam (80%) with carried forward incourse assessment (20%).
Informal assessment of weekly homework through discussions in tutorials.
Incourse 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.
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