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Module Title

LC Real Analysis

School

Mathematics

Department

Mathematics

Module Code

06 34051

Module Lead

Andrew Morris

Level

Certificate Level

Credits

20

Semester

Semester 1

Pre-requisites

Co-requisites

Restrictions

None

Exclusions

Description

Calculus is one of mankindâ€™s most significant scientific achievements, transforming previously intractable physical problems into often routine calculations. Although its roots trace back into antiquity, it was developed in the late 17th century by Newton, when developing his laws of motion and gravitation, and Leibniz, who developed the notation we still use today. Analysis is the branch of mathematics that underpins the theory behind the calculus, placing it on a firm logical foundation through the introduction of the notion of a limit. This module introduces differentiation and integration from this rigorous point of view. The notion of a function of a real variable and its derivative are formalized. The familiar techniques and applications of differentiation and integration are reviewed and extended. Simple first and second order ordinary differential equations are studied.

Learning Outcomes

By the end of the module students should be able to:

State the definition of a function and related notions and be able to sketch graphs of functions of a real variable.

Solve basic inequalities, including those involving quadratic terms and moduli.

Calculate derivatives and integrals of functions of a real variable using standard techniques.

Apply differentiation and integration in appropriate situations.

State the definition of the derivative and calculate derivatives from first principles.

State the Fundamental Theorem of Calculus and have an appreciation of its proof.

Solve simple examples of first and second order ordinary differential equations.

Construct simple proofs from definitions and standard results.

Assessment

34051-01 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions

2 hour Written Unseen January Examination (80%); In-course Assessment (20%).