Module manager: Professor S Tobias
Email: smt@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2010/11
A good grade in A-level Maths or equivalent.
This module is approved as an Elective
- Since calculus is an essential tool in many areas of mathematics, the first part of this module aims to review and consolidate the calculus covered in the core A-level syllabus. - The module also introduces hyperbolic functions which are not in the A-level core, but are covered in some A-level modules. - 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.
By the end of this module, students should be able to:
a. differentiate simple functions and determine the location and nature of turning points
b. compute the Taylor series of functions of one variable
c. use a variety of methods to integrate simple functions
d. employ several variable calculus to determine the local properties of functions of two variables.
1. Functions and their inverses: Exponential, trigonometric and hyperbolic functions and their inverses. Graphs. Addition formulas.
2. Differentiation. Definition as slope of tangent to curve. Review of basic rules of differentiation. Implicit differentiation, Chain rule. Maxima and minima. Taylor series.
3. Integration. Definite and indefinite integrals. Techniques of integration (substitution, integration by parts, reduction formulas, partial fractions).
4. Functions of several variables. Partial derivatives. Directional derivatives. Multivariable chain rule. Change of variables. Higher order derivatives. Implicit differentiation.
5. Stationary points of functions of two variables. Conditions for a stationary point. Criteria for maxima, minima and saddle points.
6. Gradients of scalar functions. Tangent planes.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | Delivery type 22 | Number 1 | Length hours 22 |
| Tutorial | Delivery type 5 | Number 1 | Length hours 5 |
| Private study hours | Delivery type 73 | ||
| Total Contact hours | Delivery type 27 | ||
| Total hours (100hr per 10 credits) | Delivery type 100 | ||
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Assessment type In-course Assessment | Notes . | % of formal assessment 15 |
| Total percentage (Assessment Coursework) | Assessment type 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Exam type Standard exam (closed essays, MCQs etc) | Exam duration 2.0 Hrs 0 Mins | % of formal assessment 85 |
| Total percentage (Assessment Exams) | Exam type 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 01/04/2011
Errors, omissions, failed links etc should be notified to the Catalogue Team