2008/09 Undergraduate Module Catalogue

MATH1932 Calculus, ODEs and Several-Variable Calculus

10 creditsClass Size: 100

Module manager: Professor S.A.E.G. Falle
Email: sam@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisite qualifications

A good grade in A-level Maths or equivalent.

This module is mutually exclusive with

MATH1400	Modelling with Differential Equations
MATH1460	Mathematics for Geophysical Sciences 1
MATH1960	Calculus
MATH1970	Differential Equations

This module is approved as an Elective

Module summary

Since calculus is an essential tool in many areas of mathematics, the first part of this module aims to review and consolidate the calculus introduced at A-level. This provides a firm foundation for the solution of first and second order ordinary differential equations. The module then goes on to develop the calculus of several variables and shows how this can be used to determine the local behaviour of functions of several variables.

Objectives

To review and develop elementary functions and differential and integral calculus. To familiarise students with simple first order and constant coefficient second order ordinary differential equations, as well as methods for their solution. To extend the differential calculus to functions of several variables. By the end of this module, students should be able to: a) Differentiate simple functions and determine their Taylor series expansion; b) Use a variety of methods to integrate simple functions; c) Solve a variety of first order and constant coefficient ordinary differential equations; d) Employ several variable calculus to determine the local properties of functions of two variables.

Syllabus

Functions and graphs. Differentiation. Taylor series. de Moivre's theorem. Exponential, trigonometric, hyperbolic functions and their inverses. Integration and techniques of integration (change of variable, partial fractions, integration by parts). First order ordinary differential equations (linear, separable). Second order ordinary differential equations with constant coefficients (homogeneous and inhomogeneous). Functions of several variable(partial derivatives, chain rule). Taylor series for functions of several variables. Critical points and criteria for maxima, minima and saddle points.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	12	1.00	12.00
Lecture	22	1.00	22.00
Tutorial	11	1.00	11.00
Private study hours			55.00
Total Contact hours			45.00
Total hours (100hr per 10 credits)			100.00

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 08/07/2008

Disclaimer

Browse Other Catalogues

• Undergraduate module catalogue
• Taught Postgraduate module catalogue
• Undergraduate programme catalogue
• Taught Postgraduate programme catalogue

Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD