| CODE | MAT2803 | ||||||||
| TITLE | Laplace and Fourier Transforms | ||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 2 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | This study-unit introduces two types of transforms, namely the Laplace Transform and the Fourier Transform, and discusses some of their main properties and applications. Laplace Transforms: - Transforms of elementary functions - Properties including linearity, scaling, shift, modulation, convolution and correlation - The Delta Function and the Unit Step function - Transforms of integrals and derivatives - Differential equations: solution of initial and boundary value problems - Impulse response and the transfer function Fourier Transforms: - Fourier's identity - Transform pairs, duality and symmetry - Fourier Sine Transform and Fourier Cosine Transform - Properties including linearity, scaling, shift, modulation, and convolution - Transforms of derivatives and integrals - Solution of boundary value problems - Parseval's Theorem Study-unit Aims: In this study-unit, the students are introduced to the concept behind the use of transforms. The main aim is to equip the students with two powerful tools, namely the Laplace transform and the Fourier transform, which can be used to handle functions when addressing engineering problems. The first transform that is studied is the Laplace transform which is applied on functions defined on the positive real domain. In the second part of this study-unit, the focus is shifted to the Fourier transform of functions defined on the whole real domain. The existence of the two types of transforms is analysed, and the Laplace transform and the Fourier transform of various functions are derived. A number of properties associated with these transforms are examined and applied to different situations. The two transforms are then used to assist in evaluating integrals and in determining the solution of initial and boundary value problems. Learning Outcomes: 1. Knowledge & Understanding: - Define and derive the Laplace transform, the Fourier transform, the Fourier Sine transform, the Fourier Cosine transform and the associated inverse transforms; - Distinguish between the different properties of Laplace transforms and of Fourier transforms; - Apply the properties of the two transforms in the appropriate contexts; - Use Laplace transforms and Fourier transforms to solve initial and boundary value problems and to evaluate integrals. 2. Skills: - Formulate solutions to problems by using appropriate mathematical techniques; - Evaluate the applicability of different theorems and results to engineering problems; - Address engineering problems by applying appropriate mathematical tools. Main Text/s and any supplementary readings: Main Textbook: - Advanced Engineering Mathematics, Peter V. O’Neil, Cengage, 7th ed. Supplementary Readings: - Spiegel M.R., 1994. Laplace Transforms, Schaum's Outline Series, McGraw-Hill, New York. - Senior T.B., 1986. Mathematical Methods in Electrical Engineering, Cambridge University Press, Cambridge. - Bracewell R.N., 2000. The Fourier Transform and its Applications, 3rd edition, McGraw-Hill, New York. |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
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| LECTURER/S | Onur Baysal |
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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 2023/4. It may be subject to change in subsequent years. |
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