| Code |
14899
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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, differentiation and integration.
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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 - First order ordinary differential equations.
2 - Higher order linear ordinary differential equations.
3 - Systems of first order linear ordinary differential equations.
4 - Laplace transforms and application to the resolution of ordinary differential equations and systems of equations.
5 - Fourier series and application to the resolution of partial differential equations.
6 - Fourier transforms.
7 - Introduction to complex analisys.
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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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Teaching Methodologies and Assessment Criteria |
The Teaching-Learning assessment consists of two tests classified for 20 values.
To obtain approval in the Curricular Unit, the student must:
- attend at least 75% of classes
- obtain a classification of at least 7 values ??in each of the tests
- the arithmetic mean of the tests must be at least 9.5 values
The classification in Teaching-Learning is given by this average rounded to the nearest unit.
All students are admitted to the Exam.
Any attempt at fraud, carried out at any time during the assessment, will result in failure in the curricular unit.
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Language |
Portuguese. Tutorial support is available in English.
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