| Code |
13934
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| Year |
3
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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 |
NA
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Learning outcomes |
(i) To understand some concepts and fundamental results from the theory of difference equations;
(ii) To use concepts and results from the theory of difference equations to analyse some specific difference equation or system of difference equations;
(iii) To recognize some examples of application of difference equations in the modelling of some phenomena in the exact sciences and social sciences;
(iv) To analyse and understand mathematical proofs;
(v) To communicate using mathematical language, written and orally.
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Syllabus |
1. Iterative Schemes
1.1 Shift operator, difference operator and anti-difference operator
1.2 Asymptotic behaviour and notions of stability
1.3 Cobweb diagrams
1.4 Periodic points, bifurcation and chaos
1.5 Sharkovsky’s Theorem
2. Scalar difference equations
2.1 Linear equations
2.2 Stability through linearization
2.3 Linear equations of higher order
2.4 Local and global stability
3. Systems of difference equations
3.1 Systems of linear equations
3.2 Stability through linearization
3.3 Planar systems
3.4 Discretization of differential equation: Euler and Runge-Kutta methods
4. Z transform
4.1 Definition and properties
4.2 Inverse transform
4.3 Equations of convolution type
4.4 Relation with Laplace and Fourier transforms
5. Asymptotic methods
5.1 Poincaré and Perron Theorems
5.2 Birkhoff’s theorem
5.3 Generalizations of Poincaré and Perron Theorems
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Main Bibliography |
- Agarwal, R.P. (1992). Difference Equations and Inequalities. New York: Marcel Dekker.
- Elaydi, S. (2005). An Introduction to Difference Equations. (3ª edição). Springer.
- Goldberg, S. (1986). Introduction to Difference Equation. New York: Dover.
- Kelley, W.G. & Peterson, A.C. (2000). Difference Equations - An Introduction With Applications. Academic Press.
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Language |
Portuguese. Tutorial support is available in English.
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