Module manager: Professor S Tobias
Email: smt@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2009/10
A good grade in A-level Maths or equivalent.
| MATH1050 | Calculus and Mathematical Analysis |
| MATH1400 | Modelling with Differential Equations |
| MATH1460 | Mathematics for Geophysical Sciences 1 |
| MATH1932 | Calculus, ODEs and Several-Variable Calculus |
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 | 22 | 1 | 22 |
| Tutorial | 5 | 1 | 5 |
| Private study hours | 73 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 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: 7/16/2010
Errors, omissions, failed links etc should be notified to the Catalogue Team