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MX3035: ANALYSIS III (2018-2019)

Last modified: 22 May 2019 17:07

Course Overview

Analysis provides the rigourous, foundational underpinnings of calculus. The focus of this course is multivariable analysis, building on the single-variable theory from MA2009 Analysis I and MA2509 Analysis II. Concepts and results around multivariable differentiation are comprehensively established, laying the ground for multivariable integration in MX3535 Analysis IV.

As in Analysis I and II, abstract reasoning and proof-authoring are key skills emphasised in this course.

Course Details

Study Type Undergraduate Level 3
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Old Aberdeen Sustained Study No
  • Dr William Turner

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?


What courses cannot be taken with this course?


Are there a limited number of places available?


Course Description

- Euclidean spaces: metric structure, topology
- Functions between Euclidean spaces: limits, continuity
- Differentiability of functions between Euclidean spaces
- The chain rule, the Inverse Function Theorem, and the Implicit Function Theorem
- Applications of differentiation


  • Euclidean spaces: metric structure, topology.
  • The Bolzano-Weierstrass theorem.
  • Functions between Euclidean spaces: limits, continuity.
  • Differentiability of functions between Euclidean spaces.
  • The chain rule.
  • The inverse function theorem.
  • The implicit function theorem.
  • Lagrange multipliers.

Course Aims

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

Main Learning Outcomes

- Understand definitions and basic concepts of real analysis (real number, limit, continuity, differential, etc.)

- Be fluent computing limits, and differentials, and manipulating elementary functions.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

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

Formative Assessment


Informal assessment of weekly homework through discussions in tutorials.


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


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