| Code |
14793
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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. First-order difference equations: Solutions, orbits, and linear equations; Stability of equilibrium points and periodic orbits; Basin of attraction and global stability; Period doubling, bifurcation, and chaos.
2. Higher-order difference equations: Difference calculus; Linear scalar equations of order ??
3. n; Method of undetermined coefficients; Asymptotic behavior of solutions; Poincaré and Perron theorems.
4. Systems of linear difference equations: Putzer's algorithm; Fundamental matrix and general solution; Jordan canonical form; Periodic linear systems: Floquet theory.
Stability of difference equation systems: Notions of stability; Stability of linear systems; Stability of periodic linear systems; Lyapunov's direct method; Stability through linearization.
5. Z-transform: Z-transform; Inverse Z-transform; Volterra systems.
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Main Bibliography |
- Elaydi, S. (2005). An Introduction to Difference Equations. (3ª edição). Springer.
- Elaydi, S. (2008). Discrete Caos. (2ª edição). Chapman & Hall/CRC.
- Kelley, W.G. & Peterson, A.C. (2000). Difference Equations - An Introduction With Applications. Academic Press.
- Goldberg, S. (1986). Introduction to Difference Equation. New York: Dover.
- Agarwal, R.P. (1992). Difference Equations and Inequalities. New York: Marcel Dekker.
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Language |
Portuguese. Tutorial support is available in English.
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