| CODE | MAT3715 | ||||||||
| TITLE | Methods of Applied Mathematics | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | The modelling of phenomena arising in fields such as classical and quantum physics, chemistry, biology and engineering is a very well-established area of applied mathematics. Examples include the diffusion of heat, vibrations in strings and membranes and the behaviour of quantum-mechanical wavefunctions. The models that describe these phenomena are very often formulated in terms of partial differential equations (PDEs). This unit will therefore focus on methods and tools that are commonly used to analyse and solve various types of PDEs. 1. Solution of partial differential equations using the method of separation of variables. 2. Fourier series and their application to solving partial differential equations. 3. Laplace and Fourier transforms and their application to solving partial differential equations. 4. The diffusion equation and its application to heat conduction. 5. The wave equation and its application to vibrating strings and membranes. 6. Laplace's equation and harmonic functions. 7. The Schrödinger equation. Study-unit Aims: The aim of this unit is to introduce students to a number of partial differential equations such as the diffusion equation, the wave equation, Laplace's equation and the Schrödinger equation. Various techniques to solve initial and boundary value problems involving these PDEs shall be discussed. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: • Understand and analyse some of the most important partial differential equations that are used to model natural phenomena • Derive and apply the fundamental properties of Fourier Series, Fourier transforms and Laplace transforms. 2. Skills: By the end of the study-unit the student will be able to: • Derive solutions to PDEs mentioned above as they appear in a variety of contexts and practical applications • Apply techniques such as the separation of variables and the use of Fourier series and integral transforms to solve these equations. Main Text/s and any supplementary readings: R. Haberman, Applied Partial Differential Equations, 4th Edition, Pearson (2003). S. Farlow, Partial Differential Equations for Scientists and Engineers, Dover (1993). E. González-Velasco, Fourier Analysis and Boundary Value Problems, Academic Press (1996). Supplementary reading: W. Strauss, Partial Differential Equations, Wiley (2008). I. Sneddon, Elements of Partial Differential Equations, Dover (2006). |
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| ADDITIONAL NOTES | Follows from: MAT1091, MAT3711 | ||||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Cristiana Sebu |
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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 2024/5. It may be subject to change in subsequent years. |
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