# 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 websiteLast updated: 08/07/2008

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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