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The University of Southampton

MATH2048 Mathematics for Engineering and the Environment Part II

Module Overview

The module aims to teach mathematical methods relevant for engineering. The first part is about differential equations and how solve them, from ordinary differential equations to partial differential equations. The second part is about either vector calculus (for Mech, Ship, Aero and ISVR) or statistics (for Civil Engineering). There are 3 lectures and 1 problem class per week. Problems are assigned each week. They are discussed in the problem class and then the solutions are posted on blackboard. Feedback and student support during module study (formative assessment) - Entire cohort: 4 on-line coursework assignments, which are marked as soon as they are completed and the corrected answers are given. Fully worked out solutions are posted on blackboard after the deadline. For Mech, Ship, Aero and ISVR: 2 additional on-line coursework. For Civil Engineering: coursework in the form of Minitab exercises - 1 class test - Lecture notes, coursework assignments, solutions and past examination papers available on the blackboard site One of the pre-requisites for MATH3083 and MATH3084

Aims and Objectives

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Demonstrate knowledge and understanding of ODE eigenvalue problems, Fourier series and transformations, Laplace transforms and partial differential equations
  • Demonstrate organisational and time-management skills
  • Critically analyse and solve some mathematical problems relevant to engineering
  • Perform calculations in simple situations and work through some longer examples
  • Demonstrate knowledge and understanding of vector calculus (Mech, Ship, Aero, ISVR)
  • Demonstrate knowledge and understanding of statistics (Civil Engineering).


• 2nd order ODEs • boundary value problems • Fourier series: real and complex • Fourier transforms • Laplace transforms • Linear partial differential equations: Classification of second order PDEs, the principle of superposition, separation of variables. Mech, Ship, Aero, ISVR only: • Vector calculus Civil Engineering only: • Further Statistics, including use of Minitab

Learning and Teaching

Teaching and learning methods

Teaching methods include • Lectures, summary notes, module blackboard site, problem classes, Minitab labs, on-line tests. Learning activities include • Individual study. • Working through the problem sheets. • Working through the coursework assignments.

Independent Study102
Total study time150

Resources & Reading list

E. Kreysig. Advanced Engineering Mathematics. 



Weekly exercises / tests and assignments


MethodPercentage contribution
Class Test 6%
Coursework 14%
Exam  (120 minutes) 80%


MethodPercentage contribution
Exam  (2 hours) 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisite: MATH1054


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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