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MX3535: ANALYSIS IV (2017-2018)

Last modified: 25 May 2018 11:16


Course Overview

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.

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
  • Professor Ben Martin

Qualification Prerequisites

  • Either Programme Level 3 or Programme Level 4

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

  • Any Undergraduate Programme (Studied)
  • MX3035 Analysis IIi (Studied)
  • Either MA2005 Introduction to Analysis (Passed) or MA2509 Analysis II (Passed)

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 and Tonelli Theorems
- Stokes's and Green's Theorems
- Introduction to Hilbert spaces

 

Syllabus

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

 

 

 

Further Information & Notes

Course Aims
To provide students with the basic knowledge of the modern mathematical analysis.
 
Learning Objectives
* Understanding definitions of the basic concepts of mathematical analysis (real number, limit, continuity, differential, integral etc).
* Fluency in computing limits, differentials and integrals and in manipulating with elementary functions.
* Understanding basic scientific applications of the mathematical concepts discussed in the course.

Degree Programmes for which this Course is Prescribed

  • BSc Applied Mathematics
  • BSc Mathematics
  • BSc Mathematics with Gaelic
  • MA Applied Mathematics
  • MA Mathematics
  • Mathematics Joint
  • Mathematics Major

Contact Teaching Time

Sorry, we don't have that information available.

Teaching Breakdown


Assessment

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.

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