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MX3535: ANALYSIS IV (2019-2020)

Last modified: 25 Sep 2019 09:58


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 Aberdeen Sustained Study No
Co-ordinators
  • Dr Alexey Sevastyanov

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

- Multivariable Riemann integration; volume of subsets of Euclidean space

- Fubini’s Theorem

- Introduction to Hilbert spaces

 

Syllabus

 

  • Multivariable Riemann integration and volumes of subsets of Euclidean space
  • Fubini’s Theorem and change of variables
  • Hilbert spaces

 

Course Aims

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


Main Learning Outcomes

By the end of this course the student should:

  • be able to state the main definitions and theorems of the course;
  • be able to prove most results from the course;
  • be familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;
  • understand integration and theorems about the Riemann integral for multivariable functions;
  • apply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.

 

 


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

Exam

Assessment Type Summative Weighting 80
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Learning Outcomes
Knowledge LevelThinking SkillOutcome
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Homework

Assessment Type Summative Weighting 10
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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Homework

Assessment Type Summative Weighting 10
Assessment Weeks Feedback Weeks

Look up Week Numbers

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Formative Assessment

There are no assessments for this course.

Resit Assessments

Best of written exam (100%) or written exam (80%) with carried forward in-course assessment (20%)

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualApplybe able to state the main definitions and theorems of the course;
ConceptualApplybe able to prove most results from the course;
ConceptualUnderstandbe familiar with the concept of Jordan measurability and understand theorems about Jordan measurable sets;
FactualUnderstandunderstand integration and theorems about the Riemann integral for multivariable functions;
ConceptualApplyapply ideas from Euclidean spaces such as inner products and convergence to the abstract setting of Hilbert spaces.

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