| Código |
15077
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| Ano |
2
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| Semestre |
S1
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| Créditos ECTS |
6
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| Carga Horária |
TP(60H)
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| Área Científica |
Matemática
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Mode of delivery |
Face-to-Face.
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Work placements |
Not applicable.
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Learning outcomes |
This Curricular Unit aims to give an introduction to the study of differential equations, Laplace transforms and Fourier series.
In the end of this Curricular Unit the student should be able to:
- classify and solve diferent types of differential equations
- solve initial value problems
- compute direct and inverse Laplace transforms. Solve differential and integral equations using Laplace transforms
- compute Fourier series of periodic functions and of functions defined in bounded intervals
- use the method of separations of variables to solve partial diferential equations
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Syllabus |
1 - Introduction to complex analysis.
2 - First order ordinary differential equations.
3 - Higher order linear ordinary differential equations.
4 - Systems of first order linear ordinary differential equations.
5 - Laplace transforms and application to the resolution of ordinary differential equations and systems of equations.
6 - Fourier series and application to the resolution of partial differential equations.
7 - Fourier transforms.
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Teaching Methodologies and Assessment Criteria |
1. The teaching methodology is based on theoretical and practical lessons. The theoretical part is based on the teacher's presentation of the syllabus contents, based on the bibliography of the unit or other notes available. Great focus will be given to the rigorous demonstration of the main results. The practical part of the classes is based on solving exercises, both in an accompanying and autonomous way.
2. The assessment is done through two written tests, carried out in the middle and at the end of the semester.
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Main Bibliography |
-An introduction to Laplace Transforms and Fourier Series, P.P.G. Dyke, Springer.
-Operational Mathematics, R. Churchill, McGraw-Hill.
-Complex Variables and Applications, R. Churchill and J. Brown, McGraw-Hill.
-Elementary Differential Equations and Boundary Value Problems, W. Boyce and R. DiPrima, Fourth Edition, John Wiley & Sons, 1986.
-Teoria Elementar de Equações Diferenciais Ordinárias, F. Pestana da Costa, IST Press, 1998.
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| Language |
Portuguese. Tutorial support is available in English.
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