# School of Mathematics and Statistics

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2013/2014 Sem. 1

## Aims

To introduce students to applied mathematics through the construction, analysis and interpretation of mathematical models for problems arising in the natural sciences, and to introduce students to the techniques of analysis used in mathematical modelling, such as numerical methods, dimensional analysis, solution of ordinary and partial differential equations.

Mathematical models from population dynamics, Newtonian dynamics and wave motion that lead to ordinary and partial differential equations are developed in detail, and the basic elements of vector calculus in three dimensions are introduced.

## Objectives

By the end of the course the students should be familiar with:

- Kinematics and the vector formulation of Newton's Laws

- Newtonian model of gravity, motion in constant gravity and particle motion under a variable force

- The energy equation as first integral of equation of motion, the concepts of kinetic and potential energy

- Motion of a particle under various forces

- P.D.E.'s, including wave equation, heat equation and Laplace equation

- Waves on a string, d'Alembert's solution, principle of superposition, application of boundary conditions, use of Fourier analysis

- Solution of algebraic equations by iterative methods

- Solution of ordinary differential equations by numerical methods

- Principles of mathematical modelling

- Basic vector calculus including the differential operators div, grad and curl

- Integration involving vector quantities, Green's Theorem, Stokes's Theorem and Divergence Theorem.

`NEWTON      D'ALEMBERT     FOURIER      STOKES       LAPLACE`

## Syllabus

An outline of the syllabus is as follows:

Mathematical Modelling (10 lectures)

Newtonian Mechanics (7 lectures)

Numerical Methods (8 lectures)

Vector Calculus (17 lectures)

Partial Differential Equations (9 lectures)

## Textbooks

Advanced Engineering Mathematics E Kreyszig; Wiley, 2001.

Vector Analysis M R Spiegel; McGraw-Hill; 1959.

## Lectures, practicals and tutorials

The average load, in hours per week, is as follows:

Lectures: 5

Maths lab: 2

These figures do not include the revision & exam period at the end of each semester.

## Assessment

30% of the assessment mark is from continuous assessment during the semester; 70% is from a 3 hour exam at the end of the semester.

Re-assessment is entirely by a 3 hour exam in August.

## Prerequisites

MT1002 and MT2001

## Availability

This module is taught every year in Semester 2 at 12.00.

## Lecturers

Dr A N Wright (Module coordinator), Dr A P Naughton, Dr A L Haynes