Last modified: 24 Jun 2020 14:31
Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on MX3035 Analysis III, continuing the development of multivariable calculus, with a focus on multivariable integration. Hilbert spaces (infinite dimensional Euclidean spaces) are also introduced.
Students will see the benefit of having acquired the formal reasoning skills developed in Analysis I, II, and III, as it enables them to work with increasingly abstract concepts and deep results. Techniques of rigourous argumentation continue to be a prominent part of the course.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
- Multivariable Riemann integration; volume of subsets of Euclidean space
- Fubini’s Theorem
- Introduction to Hilbert spaces
To provide students with the basic knowledge of the modern mathematical analysis.
Main Learning Outcomes
By the end of this course the student should:
Information on contact teaching time is available from the course guide.
Three x standard course assignments - 33.33% each
Alternative Resit Arrangements for students taking course in Academic Year 2020/21
Resubmission of failed elements (pass marks carried forward)
There are no assessments for this course.
|Knowledge Level||Thinking Skill||Outcome|
|Factual||Apply||be able to state the main definitions and theorems of the course;|
|Conceptual||Apply||be able to prove most results from the course;|
|Conceptual||Understand||be familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;|
|Factual||Understand||understand integration and theorems about the Riemann integral for multivariable functions;|
|Conceptual||Apply||apply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.|