The University of Southampton

MATH2008 Introduction to Applied Mathematics

Module Overview

This module is designed to provide students with a basic appreciation of traditional applied mathematics. It assumes no prior knowledge of applied mathematics. It provides the foundation needed for studying applied mathematics at a more advanced level as well as an interesting self contained module for those students who do not wish to take other applied mathematics modules subsequently. The module focuses on Newtonian dynamics, one of the great intellectual developments in history, which provides a beautiful description of many physical situations. Applications include fluid flow, rockets, fairground rides, Halley’s comet, the weather and even doing your laundry!

Aims and Objectives

Module Aims

• To give the student an introduction to basic concepts in Newtonian mechanics, without assuming any prior knowledge • To give the student the basic mathematical skills to analyse problems involving the motion of particles in three dimensions.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Understand the concepts of relative velocity and of gravitational and frictional forces
  • Find the velocity and acceleration of a particle using Cartesian, cylindrical polar and spherical polar coordinates
  • Recall and apply the concept of the Lagrangian in simple situations
  • Derive and solve the differential equations arising from Newton’s laws of motion applied to simple situations using vector notation
  • Manipulate and understand derivatives of vectors and line integrals
  • Understand and exploit the conservation laws of momentum and energy for simple situations


PHYSICAL BACKGROUND:Revision of vectors, position/velocity/acceleration components, Galilean transformation, time/space/events/observers, relative velocity. FORCES:Force, moments, centre of mass, equilibrium, Newton’s laws, constant forces, gravitation, friction, elastic springs, air resistance, tension. DYNAMICS & IMPULSES:Conservation of mass, linear momentum, collisions, rocket motion. FORCE FIELDS & ENERGY:Vector fields, revision of grad/div/curl, line integrals, conservation of energy, conservative forces, work, stability. ANALYTICAL DYNAMICS: The calculus of variations, lagrangians, the Euler-lagrange equations

Learning and Teaching

Independent Study104
Total study time150

Resources & Reading list

There is a wide range of books that may be consulted. Details will be given at the beginning of the module.. 

Gregory Douglas R. Classical Mechanics. 



MethodPercentage contribution
Class Test 5%
Coursework 15%
Written exam  (2 hours) 80%

Linked modules

One of the pre-requisites for MATH2044, MATH3071, MATH3072 and MATH6149


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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