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MX3035: ANALYSIS III (2017-2018)

Last modified: 23 Aug 2017 15:33


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
Co-ordinators
  • 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?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

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

 

Syllabus

  • 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.

Further Information & Notes

Course Aims

To provide students with a basic knowledge of modern mathematical analysis.
 
Learning Objectives
-Understand definitions and basic concepts of real analysis (real number, limit, continuity, differential, integral, etc.)
-Be fluent computing limits, differentials, and integrals, and manipulating elementary functions.

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

1 two-hour written examination (80%); 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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