Last modified: 13 Aug 2020 11:50
Analysis provides the rigorous, foundational underpinnings of calculus. This course builds on the foundations in Analysis I, and explores the notions of differential calculus, Riemann integrability, sequences of functions, and power series.
The techniques of careful rigorous 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  Aberdeen  Sustained Study  No 
Coordinators 

 Differentiation of functions of one variable: basic definitions and properties, chain rule, basic results on differentiable functions, Rolle's Theorem, Mean Value Theorem.
 Riemann integrability: Riemann sums, basic properties, the Fundamental Theorem of Calculus, improper integrals  Sequences of functions: pointwise convergence, uniform convergence, properties of limits of functions, series of functions
 Power series: convergence, continuity, differentiability, integrability, Taylor series
Syllabus
Course Aims
To further develop understanding of the concepts, techniques, and tools of calculus. Calculus is the mathematical study of variation. This course emphasises differential and integral calculus, sequences and series of functions.
Learning Objectives
By the end of this course the student should:
Information on contact teaching time is available from the course guide.
Ten x weekly mutichoice or short answer online quizzes  2% each
Two a standard course assessments  25% and 30%
Essaystyle assignment  25%
There are no assessments for this course.
Knowledge Level  Thinking Skill  Outcome 

Factual  Understand  be able to state the main definitions and theorems of the course; 
Factual  Apply  Be able to prove most results from the course; 
Conceptual  Understand  be familiar with the concept of differentiability and understand theorems about differentiable functions; 
Factual  Understand  understand Riemann integration and theorems about the Riemann integral; 
Conceptual  Apply  Be able to apply techniques for showing integrability or nonintegrability of functions; 
Conceptual  Apply  Be able to distinguish between pointwise and uniform convergence of sequences of functions 
Factual  Analyse  Be able to compute Taylor series, compute the interval of convergence of power series, and use Taylor's theorem to estimate functions by polynomials. 
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