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.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
- 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
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.
By the end of this course the student should:
Information on contact teaching time is available from the course guide.
There are no assessments for this course.
|Assessment Weeks||Feedback Weeks|
|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 non-integrability 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.|