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Module title Numerical Methods
Module code CENV2026
Module lead

Mithila Paththini Marakkala

Module lead profile url:
External Examiner: Professor Zoran Kapelan, University of Exeter
Faculty Engineering & the Environment
Academic unit CivEng and the Env
Academic session first offered 201213
Credit Points ECTS 7.5
Level Undergraduate
When will the module be taught Semester 2
Pre-requisite and/or co-requisite modules
Programmes in which the module is core
Programmes in which the module is compulsory BEng Civil Eng with Architect (year 2)
BEng Civil Engineering (year 2)
MEng Civil Eng w Placement (year 2)
MEng Civ Env Eng w Placement (year 2)
MEng Civil & Environmental Eng (year 2)
MEng Civil Eng w Yr in Indust (year 2)
MEng Civil Engineering (year 2)
MEng Civil Eng & Architecture (year 2)
MEng Civ Eng Arch w Placement (year 2)
Programmes in which the module is optional
Date of last edit 16th Sep 2016 - 8:41am

Module overview

This module provides an in depth coverage of key numerical methods to solve practical mathematical problems that occur throughout engineering. The module consists of two main parts:

  1. The course demonstrates the use of numerical analysis as a powerful problem solving tool in engineering. The course encompasses Numerical Analysis, Regression Analysis, Taylor Series and Applications, Numerical Integration and Solutions to Ordinary Differential Equations, with applications to engineering problems through computational simulations using a commercial package, MATLAB.
  2. The course also provides an introduction to the theory underlying the finite element (FE) method, with applications through computational simulations for a range of engineering problems using a commercially available general-purpose finite element package, ABAQUS.

Computer lab exercises and assignments will give opportunity for students to analyse and solve a number of practical engineering problems.


Pre-requisite module - MATH1054.

Aims and learning outcomes


Having successfully completed this module, you will be able to:

  • To give students a thorough understanding of key numerical analysis methods and their application to solve common engineering problems.
  • To provide the students with skills to understand the significance, calculation and interpretation of numerical errors and convergence criteria associated with numerical analysis.
  • To train students to write, implement, test and evaluate computer programs (using the MATLAB platform) to solve a range of problems numerically.
  • To provide students with a knowledge and understanding of the fundamental theoretical basis of the FE method and its application in analysis of 1D and 2D engineering problems.

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • Numerical analysis techniques available to solve a range of mathematical problems encountered in engineering (root finding, regression analysis, Taylor series, differentiation and integration, solution of ODEs)
  • The significance, calculation and interpretation of numerical errors and methods to eliminate or mitigate their effects.
  • The fundamental concepts of the FE method.
  • The theory of the formulation and solution of finite element models.
  • The key steps required to complete a FE simulation.
  • The limitations of the FE method and appropriate choice of element type to suit the problem.

Subject Specific Intellectual

Having successfully completed this module, you will be able to:

  • Recognise engineering problems that may be solved numerically.
  • Select the appropriate numerical solution technique to solve the problem.
  • Apply concepts of numerical analyses and FE models for analysis and solving of real-life engineering problems.
  • Develop and solve FE simulations.
  • Demonstrate the accuracy of typical numerical and FE results.

Transferable and Generic

Having successfully completed this module, you will be able to:

  • Logical thinking and conceptualisation of a problem for solution by computer algorithm.
  • Ability to use the MATLAB programming platform including built-in functions.
  • Presentation of data and analysis results.
  • Critical analysis and judgment as to the quality of computer analysis output.
  • Learning the use of commercial FE software.
  • Time management and independent learning.

Subject Specific Practical

Having successfully completed this module, you will be able to:

  • Write, compile, execute and test programs using MATLAB to solve a range of problems numerically.
  • Use MATLAB built-in functions in a range of contexts relating to problem solving in numerical analysis.
  • Use a commercial FE package to solve practical 1D and 2D engineering problems (including understanding of the pre-processing, solution and post-processing phases of the process).
  • Utilise user manuals and online help pages/tutorials to learn and gain familiarity with commercial software platforms.

Graduate Attributes

Graduate Attributes are the personal qualities, skills and understandings that University of Southampton students have the opportunity to develop. They include but extend beyond subject-specific knowledge of an academic discipline and its technical proficiencies. The Graduate Attributes are achieved through the successful attainment of the learning outcomes of the programmes, and successful engagement with the University’s co-curriculum e.g. the Graduate Passport.

A checklist for embedding the graduate attributes is available at:

Summary of syllabus content

Numerical analysis (10 lectures + 2hrs tutorials + 8hrs computer labs) ~ 6.5 credits

1. Introduction to numerical analysis and the use of MATLAB as a numerical tool (1L)


2.  Root finding (2L)

  • Direct and iterative methods
  • Newton–Raphson method
  • Round-off and Truncation errors
  • MATLAB in-built functions


3.  Regression analysis (2L)

  • Polynomials, Least squares analysis, Chebyshev polynomials, MATLAB in-built functions


4.  Taylor series and applications (1L)


5.  Numerical differentiation and integration (2L)

  • Motivation and objectives
  • Numerical differentiation (first derivative, second derivative)
  • Numerical integration (Trapezoidal rule, Mid-point rule)
  • MATLAB in-built functions


6.  Solution to Ordinary differential equations (ODE) (2L)

  • Introduction to ODE and their occurrence in engineering problems
  • Finite difference methods
  • Euler Method, Runge–Kutta methods
  • Applications using MATLAB


MATLAB computer lab (Weeks 3-6) (4 x 2hrs)

  • Weeks 3, 4 & 5 – Programming using MATLAB
  • Week 6 – Assignment


Finite element analysis (14 lectures + 4hrs tutorials + 8hrs computer labs) ~ 8.5  credits


1.  Introduction (1L)


2.  Finite Element Method (1L)

  • Problem clarification, modelling and discretisation
  • Elements, nodes and degrees of freedom, meshes


3.  Getting started with ABAQUS/Standard (1L)


4. Elastic rods and beams(5L)

  • Truss elements
  • Beam elements
  • Element stiffness
  • Assembly of elements
  • Global stiffness matrix and its characteristics
  • Direct formulation (stiffness method)
  • Solution of structure equations


5. Concept generalization to two dimensions (6L)

  • Preliminaries (Stress–strain relationship, Stress–displacement relationship, Compatibility, Equilibrium equations, Boundary conditions, Exact and approximate solutions)
  • Interpolation and shape functions
  • Formulation of element matrices (Linear (constant strain) triangle, Quadratic rectangle)
  • Isoparametric element formulations (Bilinear quadrilateral, Quadratic quadrilateral)
  • Limitations associated with different types of elements


ABAQUS computer labs and tutorials (Weeks 7-10) (4 x 2hrs)

  • Week 7, 8, 9 – Problem solving using ABAQUS
  • Week 10 – Assignment


Worked examples (Computer Labs):

  1. 2D truss
  2. 2D plane stress analysis

Summary of teaching and learning methods

Teaching methods include

  • Lectures
  • Computer lab supervisions
  • Tutorials and worked examples

Learning activities include

  • Lectures and tutorials
  • Computer lab classes
  • Problem assignments
  • Private study

PowerPoint slides available from Blackboard

Study Time allocation:

Contact hours: 44 hours

Private study hours: 106 hours

Total study time: 150 hours

Summary of assessment and Feedback methods

Assessment Method Number % contribution to final mark Final assessment (✔)
Assignment 1 (programming using MATLAB) 20%
Assignment 2 (FE analysis using ABAQUS) 20%
Exam      (Duration:90 minutes) 60%

Referral Method

By examination and a new coursework assignment

Final exam (90 mins) = 60%

Assignment 1 (programming using MATLAB) = 20%

Assignment 2 (FE analysis using ABAQUS) = 20%

Method of Repeat Year

Repeat year internally

Repeat year externally

Learning Resources

Resource type: Core textbook

R. J. Schilling and S. L Harris, Applied Numerical Methods for Engineers using MATLAB and C, Brooks/Cole Publishing, USA, 2000

Resource type: Core textbook

D. Faires and R. Burden, Numerical Methods (4th edition), Brooks / Cole, USA

Resource type: On-line resources

Mathworks website:

Resource type: Core textbook

S. J. Chapman, MATLAB Programming with Applications for Engineers

Resource type: Core textbook

R.D. Cook, Concepts and Applications of Finite Element Analysis, John Wiley & Sons, 1981

Resource type: Core textbook

K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1996

Resource type: Other

ABAQUS user manual

Cost Implications



  • A range of standard construction materials are provided to support the design projects within this module. However, students are encouraged to develop unique designs and choose alternative materials, the costs of which will be covered by the Faculty should they be deemed appropriate and clearly presented by a given cut-off date. The costs of additional materials and components identified after this date would be borne by the student group. (equipment)
  • Students are expected to cover the costs associated with the printing of drawings and graphic presentations. These are typically expected to be of the order of £50 per group (typically five students per group), also depending on the quality of printing chosen. Two CDs to submit computer codes to be covered by the each student. (printing-and-copying)

Appendix: KIS hours

Contact hours for Teaching:Hours
Seminars (including sessions with outside speakers)0
Practical Classes and Workshops (including Boat work)0
Project supervision0
Demonstration Sessions0
Supervised time in studios/workshops/laboratories16
External Visits0
Summer Workshops0
Work Based Learning0
Independent studyHours
Preparation for scheduled sessions12
Follow-up work12
Wider reading or practice-7
Completion of assessment task79
Placement Hours0
Year Placement0
6 Month Placement0