| Code |
8546
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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 |
Non 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 |
1- The assessment may be conducted during the teaching-learning period (continuous assessment) or through a final exam.
2- Assessment of knowledge during the teaching-learning period: two tests, each worth 9 points, on October 27, 2025, and November 27, 2025, and a mini-test, in the last class of the semester, worth 2 points.
3- Students who obtain a minimum of 3 points on each test, a combined score of 9.5 points on both tests and the mini-test, and a 70% attendance rate (50% for repeating students and 0% for working students) will be exempt from the final exam.
4- Only students with a 70% attendance rate (50% for repeating students and 0% for working students) will be admitted to the exam. Attendance will be recorded from the first class onwards.
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Language |
Portuguese. Tutorial support is available in English.
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