| Code |
14907
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| Year |
2
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| Semester |
S2
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| ECTS Credits |
6
|
| Workload |
TP(60H)
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| Scientific area |
Physics
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|
Entry requirements |
None
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|
Learning outcomes |
Complement and reinforce training in mathematics, namely in areas necessary for the full understanding of classic and modern topics in Physics.
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|
Syllabus |
1 - Fourier transforms
Complex Fourier series.
Fourier transform.
Inverse transformation.
Parseval's Theorems and Convolution Theorem.
Fourier integral theorem.
Dirac Delta function.
2 -Partial differential equations
Cylindrical and spherical coordinates
Differential operators
Separation of variables
Wave equation
Laplace and Poisson equations
Diffusion equation
Green functions
3 - Special Functions
Sturm-Liouville problem
Polynomials of Legendre, Hermite and Laguerre
Bessel functions.
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Main Bibliography |
1. Arfken GB, Weber HJ, Harris FE (2012). Mathematical Methods for Physicists, 7th ed. New York: Academic Press
2. Braun M (1993). Differential Equations and Their Applications, 4th ed. New York: Springer
3. Cantrell CD (2000). Modern Mathematical Methods for Physicists and Engineers. New York: Cambridge University Press
4. Ramos M (2011). Curso Elementar de Equações Diferenciais, 3.ª ed. Lisboa: Universidade de Lisboa
5. Riley KF, Hobson MP, Bence JS, Mathematical Methods fpr Physics and Engineering, 3rd ed, New York: Cambridge University Press
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Teaching Methodologies and Assessment Criteria |
The classes will be theoretical-practical: the theoretical contents exposed will be illustrated with examples that clarify the concepts, methods and results presented. In addition to 2 written tests, the assessment includes students' solving exercises/homework, with presentation and discussion.
Evaluation of the teaching-learning period:
The presentation of solved exercises/homeworks - 40%
Simple arithmetic mean of 2 written tests - 60%
Final exam.
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Language |
Portuguese. Tutorial support is available in English.
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