Course Details in 2023/24 Session

Module Title	LC Real Analysis & the Calculus (30 credit)
School	Mathematics
Department	Mathematics
Module Code	06 30303
Module Lead	Chris Good
Level	Certificate Level
Credits	30
Semester	Semester 1
Pre-requisites
Co-requisites	LC Vectors, Geometry & Linear Algebra - (06 30305)
Restrictions	Available to only students on the Jinan Maths programmes
Exclusions
Description	The calculus is one of mankind’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. The theory of infinite sequences and series, including Taylor series, is introduced.
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. State the definition of convergence for sequences and series. Determine the convergence of various sequences and series using the algebra of limits and other standard techniques. State the Taylor series of common functions and calculate Taylor series of functions. Construct simple proofs from definitions and standard results.
Assessment	30303-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	Assessment: 3 hour examination (80%), work done during semester (20%) Reassessment: best of 3 hour resit examination (100%) or 3 hour resit examination (80%) and work done during the semester (20%) Attendance at tutorials is a required element of this module.
Other
Reading List