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### 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 Level Undergraduate 3 First Sub Session 15 credits (7.5 ECTS credits) Old Aberdeen No Dr William Turner

### Qualification Prerequisites

• Either Programme Level 3 or Programme Level 4

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

• Either MA2005 Introduction to Analysis (Passed) or MA2009 Analysis I (Passed)

None.

None.

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### 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.

Course Aims

### 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.

### 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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