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: 2016/17
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

Supervisor: Prof Edd Codling, email:
Teaching Staff: Prof Edd Codling, email:
Contact details: Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email

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.


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.


10 per cent Coursework Mark, 90 per cent Exam Mark


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.


  • Essential Reading:
  • J. Gilbert; C. Jordan, Guide2 Mathematical Methods, Palgrave Macmillan, 2002
  • Background Reading:
  • E. Swokowski, M. Olinick & D. Pence, Calculus, PWS Publishing Co, any edition
  • R. Adams and C. Essex, Calculus (A Complete Course), Pearson

Further information