# Study-Unit Description

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CODE CVE5644

TITLE Numerical Techniques in Engineering

LEVEL 05 - Postgraduate Modular Diploma or Degree Course

ECTS CREDITS 5

DEPARTMENT Civil and Structural Engineering

DESCRIPTION This study-unit introduces numerical techniques which are used to solve engineering problems. The study-unit addresses numerical techniques of approximations, such as polynomial interpolation, the least squares method, and numerical differentiation and integration, the solution of non-linear equations, and ordinary and partial differential equations. The study-unit introduces finite difference, and finite elements techniques, using simple IT and programming tools. One emphasis of the study-unit will be on methods of validating computer solutions to engineering problems.

Study-unit Aims:

The study-unit aims to introduce students to the tools of numerical approximation to the solutions of engineering problems, and therefore to an understanding of modern computer tools of analysis. At the same time, however, it aims at highlighting the limitations of numerical methods, and the importance of validating analytical models and computer output using approximate methods of engineering analysis.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:
- Identify the basic principles of numerical approximations for the solution of non-linear equations, and of ordinary and partial differential equations;
- Explain the theoretical basis of finite difference and finite element techniques, as well as the limitations and pitfalls of such numerical modelling;
- Discuss the limitations and difficulties of "rigorous" analysis of indeterminate structures;
- Formulate finite element equations and element stiffness matrices;
- Synthesize the iso-parametric concept as applied to 1D, 2D and 3D elements.

2. Skills:

By the end of the study-unit the student will be able to:
- Apply numerical techniques such as the least squares method, and numerical differentiation and integration, to solve non-linear equations, and ordinary and partial differential equations;
- Use simple computer software to undertake numerical solutions for simple engineering problems;
- Apply simple approximate techniques of structural analysis of indeterminate structures to verify proposed analytical models, and validate the output of numerical analysis;
- Interpret computer output and correlate with approximate analysis.

Main Text/s and any supplementary readings:

- Gerald, C.F., (1978) Applied Numerical Analysis, 2nd ed., Addison Wesley, Ontario.
- de Vahl Davis, G., (1986), Numerical Methods in Engineering and Science, Chapman and Hall, London.
- Noble, B., (1964), Numerical Methods: 2; Differences, Integration and Differential Equations, Oliver and Boyd, London.
- Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T., (1992), Numerical Recipes : The Art of Scientific Computing (Fortran Version), Cambridge University Press, Cambridge.
- Ghali, A. & Neville, A.M., (1978), Structural Analysis – A Unified Classical and Matrix Approach, 2nd ed., Chapman and Hall, London.
- Brohn,D., (2005), Understanding Structural Analysis, BSP Professional Books.

STUDY-UNIT TYPE Lecture, Independent Study & Tutorial

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Examination (2 Hours) SEM2 Yes 100%

LECTURER/S Marc Bonello

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2021/2. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit