# 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

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

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