| Code |
15758
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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 - Introduction to Complex Analysis.
2 - Ordinary differential equations of first order.
3 - Ordinary linear differential equations of higher order than the first.
4 - Systems of linear ordinary differential equations of first order.
5 - Laplace transforms and application to the resolution of ordinary differential equations and systems of ordinary differential equations.
6 - Fourier series and application to solving partial derivatives equations.
7 - Fourier Transforms.
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Main Bibliography |
R. Churchill, Operational Mathematics, McGraw-Hill
R. Churchill and J. Brown, Complex Variables and Applications, McGraw-Hill
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Fourth Edition, John Wiley & Sons, 1986
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Teaching Methodologies and Assessment Criteria |
Classes are theoretical-practical, where after presenting the main results, they are illustrated with examples and exercises.
Students are provided with support sheets and exercises to work at home.
The Teaching-Learning Assessment consists of three tests, T1, T2 and T3, rated for 20 values.
The Teaching-Learning classification is calculated as follows EA=0.3*T1+0.35*T2+0.35*T3.
Students with EA greater than or equal to 9.5 and less than 17 are exempt from the exam and with a final grade EA; and those with an EA greater than or equal to 17 are invited to a supplementary test.
Students with EA less than 3 values are not admitted. Finalist students and student workers are Admitted to the Exam.
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Language |
Portuguese. Tutorial support is available in English.
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