# Module Details

## MA118-4-SP-CO: Further Calculus

Note: This module is inactive. Visit the Module Directory to view modules and variants offered during the current academic year.

Year: 2017/18
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Outside Option: No

Staff
Supervisor: Professor Edward Codling
Teaching Staff: Prof Edd Codling, email: ecodling@essex.ac.uk
Contact details: Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email cmwatts@essex.ac.uk

 Module is taught during the following terms Autumn Spring Summer

### Module Description

This course extends ideas from MA104, continuing with complex numbers, differential equations, and introducing limits, partial differentiation and its applications.

Syllabus

Complex numbers:
- representation, Argand diagram;
- modulus and argument;
- de Moivre's theorem, complex nth roots.

Ordinary differential equations:
- second-order linear differential equations with constant coefficients;
- general, complementary and particular solutions.

Limits and continuity:
- formal rules and pictorial interpretations;
- l'Hopital's rule;
- continuity at a point.

Partial differentiation:
- calculation of first- and second-order partial derivatives of elementary functions of two or three variables;
- finding and classifying the stationary points of a function of two variables;
- chain rule for first-order partial differentiation of functions of two or three variables;
- gradient of a scalar field in two or three dimensions;
- calculate the directional derivative.

On completion of the course students should be able to:
- move between Cartesian and polar forms of complex numbers; calculate arguments, moduli and complex conjugates;
- plot complex numbers on Argand diagrams;
- multiply and divide complex numbers in polar form;
- find complex nth roots
- solve second-order linear differential equations with constant coefficients, find general and particular solutions;
- calculate limits of elementary functions;
- use l'Hopital's rule;
- find partial derivatives of elementary functions of two and three variables;
- use the chain rule for first-order partial differentiation;
- find directions of steepest slope for functions of two or three variables.

### Learning and Teaching Methods

This course consists of 30 contact hours given at 3 hours per week commencing in week 16. There is a test at the end of term and five assessed problem sheets throughout the term. There are three revision lectures in the summer term.

### Assessment

10 per cent Coursework Mark, 90 per cent Exam Mark

### Coursework

The coursework is assessed by five equally-weighted pieces of homework.

### Other details

Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information

### Exam Duration and Period

1:30 during Summer Examination period.

### Other information

'A' level Maths or equivalent normally required. Only available together with MA104. Available independently to Socrates /IP students spending all relevant terms at Essex.