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# Module details

## MA104-4-AU: CALCULUS

Year: 2013/14
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes

Staff
Supervisor: Dr Dan Brawn, email: dbrawn@essex.ac.uk
Teaching Staff: Dr Dan Brawn, email: dbrawn@essex.ac.uk
Contact details: Miss Camilla Thomsen, Departmental Administrator, Tel. 01206 873040, email cthomsj (Non essex users should add @essex.ac.uk to create the full email address)

 Module is taught during the following terms Autumn Spring Summer

### Module Description

This course revises ideas associated with continuous functions, including the idea of an inverse, differentiation and integration, and sets them in a more fundamental context which permits a better understanding of their properties. Differential equations are introduced, and methods for solving them are studied. The properties of inequalities are reviewed. Complex numbers in Cartesian form are introduced.

Syllabus

Geometry and Trigonometry:

- Pythagoras' theorem; trigonometric functions.

- Basic manipulation of inequalities

Functions of one variable:

- the functions exp, ln, xa, |x|, trigonometric and hyperbolic functions; their domains and their graphs;

- power laws; exp(x+y), ln(xy);

- derivatives of xa, exp, sin, cos, ln;

- differentiation of sums, products and quotients;

- function of a function; chain rule for differentiation;

- inverse functions;

- stationary points;

- indefinite integrals as antiderivatives; definite integrals; improper integrals;

- division of polynomials, partial fractions, integration of rational functions;

- integration by parts and by substitution

- first order differential equations; separation of variable and integrating factor.

Complex numbers:

- addition, subtraction, multiplication and division in Cartesian form

- the Argand diagram

On completion of the course, students should be able to:

- be able to use Pythagoras's Theorem and the basic concepts of trigonometry;

- be familiar with elementary functions, the basic rules of the differential and integral calculus for functions of one variable;

- be familiar with the idea of a domain of definition and an inverse function;

- be able to manipulate inequalities;

- add, subtract, multiply, and divide complex numbers in Cartesian form;

- plot complex numbers on an Argand diagram;

- solve first order differential equations.

### Learning & Teaching Methods

This course consists of 30 contact hours given at 3 hours per week commencing in week 2 (the first teaching week). There will be a test at the end of term and five assessed problem sheets throughout the term. Three revision lectures will also be given in the summer term.

### Assessment

25 per cent Coursework Mark, 75 per cent Exam Mark

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

### Exam Duration and Period

1:30 hour exam during Summer Examination period.

### Other information

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

### Bibliography

• Recommended text:
• Palgrave Macmillan: Guide Mathematical Methods 9780333794449 J. Gilbert; C. Jordan
• Supplementary texts:
• E. Swokowski, M. Olinick & D.Pence, "Calculus", PWS Publishing Co.