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MX3535: ANALYSIS IV (2018-2019)

Last modified: 22 May 2019 17:07


Course Overview

Analysis provides the rigorous, 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 rigorous argumentation continue to be a prominent part of the course.

Course Details

Study Type Undergraduate Level 3
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Old Aberdeen Sustained Study No
Co-ordinators
  • Dr Alexey Sevastyanov

Qualification Prerequisites

  • Either Programme Level 3 or Programme Level 4

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

- Multivariable Riemann integration; volume of subsets of Euclidean space

- Fubini's Theorem

- Introduction to Hilbert spaces

Syllabus

  • Multivariable Riemann integration and volumes of subsets of Euclidean space
  • Fubini and Tonelli theorems
  • Hilbert spaces

Course Aims

To provide students with the basic knowledge of the modern mathematical analysis.


Main Learning Outcomes

By the end of this course the student should:

  • be able to state the main definitions and theorems of the course;
  • be able to prove most results from the course;
  • be familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;
  • understand integration and theorems about the Riemann integral for multivariable functions;
  • apply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.

Degree Programmes for which this Course is Prescribed

None.

Contact Teaching Time

32 hours

This is the total time spent in lectures, tutorials and other class teaching.

Teaching Breakdown

  • 2 Lectures during University weeks 25 - 35
  • 1 Tutorial during University weeks 26 - 35

More Information about Week Numbers


Summative Assessments

1st attempt - 1 two-hour written examination (80%); in-course assessment (20%).

Resit – 1 two-hour written examination paper. Maximum of written exam (100%) or written exam (80%) with carried forward in-course assessment (20%).

Formative Assessment

 

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course 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.

Course Learning Outcomes

None.

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