| Code |
16146
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Knowledge of real functions with several variables, derivation and integration.
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Learning outcomes |
This curricular unit is an introduction to the study of differential equations, Laplace transforms and Fourier series.
At the end of the course unit the student should be able to:
- distinguish and solve the different types of differential equations
- solve initial value problems
- calculate direct and inverse Laplace transforms of usual functions. Solve differential and integral equations using Laplace transforms
- determine Fourier series of periodic functions and functions defined in bounded intervals
- use the method of separation of variables in obtaining solutions to partial derivative problems
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Syllabus |
1 - Ordinary differential equations of first order.
2 - Ordinary linear differential equations of higher order than the first.
3 - Systems of linear ordinary differential equations of first order.
4 - Laplace transforms and application to the resolution of ordinary differential equations and systems of ordinary differential equations.
5 - Fourier series and application to solving partial derivatives equations.
6 - Fourier Transforms.
7 - Introduction to Complex Analysis.
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Main Bibliography |
1 - R. Churchill, Operational Mathematics, McGraw-Hill.
2- R. Churchill and J. Brown, Complex Variables and Applications, McGraw-Hill.
3- W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, Fourth Edition, John Wiley & Sons, 1986.
4--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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