Code |
14793
|
Year |
3
|
Semester |
S1
|
ECTS Credits |
6
|
Workload |
TP(60H)
|
Scientific area |
Mathematics
|
Entry requirements |
NA
|
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.
|
Syllabus |
1. 1st order difference equations 1.1 Linear Equations; 1.2 Spider web diagrams and stability of equilibrium points; 1.3 Stability of periodic orbits; 1.4 Bifurcation and Sharkovsky's Theorem; 1.5 Basin of attraction and global stability.
2. Scalar difference equations 2.1 Shift, difference and anti-difference operators; 2.2 Homogeneous and non-homogeneous linear equations; 2.3 Asymptotic behavior.
3. Systems of difference equations 3.1 The discrete Putzer algorithm; 3.2 Fundamental matrix and variation of the constants formula; 3.3 Autonomous systems: Jordan's canonical form; 3.4 Periodic linear systems: Floquet exponents.
4. Stability of difference equation systems 4.1 Stability of linear systems; 4.2 Stability through linearization; 4.3 Lyapunov stability theorem and LaSalle's invariance principle.
5. Z Transform 5.1 Definition and properties; 5.2 Inverse transform; 5.3 Convolution-type equations.
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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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