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  6. MX3035: ANALYSIS III

MX3035: ANALYSIS III (2017-2018)

Last modified: 25 May 2018 11:16


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
Term First Term 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?

  • Any Undergraduate Programme (Studied)
  • Either MA2005 Introduction to Analysis (Passed) or MA2009 Analysis I (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

 

- 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.

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 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

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.

Course Learning Outcomes

None.
 

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