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Course Overview

Analysis provides the rigourous, foundational underpinnings of calculus. It is centred around the notion of limits: convergence within the real numbers. Related ideas, such as infinite sums (a.k.a. series), continuity, differentiation, and Riemann integration, are also visited in this course.

Care is needed to properly use the delicate formal concept of limits. At the same time, limits are often intuitive, and we aim to reconcile this intuition with correct mathematical reasoning. The emphasis throughout this course is on rigourous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.

Course Details

Study Type Level Undergraduate 2 First Sub Session 15 credits (7.5 ECTS credits) None. No Dr Aaron Tikuisis

Qualification Prerequisites

• Programme Level 2

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Course Description

• Fundamental properties of real numbers: field operations, order, completeness.
• Sequences and limits: convergence, basic examples, decimal representation of real numbers.
• Functions of one real variable: limits and continuity, elementary functions, basic results on continuous functions.
• Differentiation of functions of one variable: basic definitions and properties, chain rule,basic results on differentiable functions
• Integration of functions of one variable: basic definitions and properties, the fundamental theorem of calculus, application to arc lengths of plane curves.

Degree Programmes for which this Course is Prescribed

• BSc Applied Mathematics
• BSc Mathematics
• BSc Mathematics & Engineering Mathematics
• BSc Mathematics with Gaelic
• MA Applied Mathematics
• MA Mathematics
• MA Mathematics with Computing
• Master of Physics with Complex Systems Modelling
• Mathematics Joint
• Mathematics Major
• Mathematics Minor

Contact Teaching Time

Sorry, we don't have that information available.

Assessment

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

Resit: 1 two-hour written examination paper. The CAS mark awarded will be the maximum of 100% resit and 80% resit with 20% in-course assessment.

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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