| Code |
14787
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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 concepts and fundamental results from the theory of ordinary and partial differential equations;
(ii) To use results from ordinary differential equations theory to analyse equations or systems of ordinary differential equations;
(iii) To understand and to use some results from partial differential equations theory, with incidence in the wave, heat and Laplace equations;
(iv) To analyse and understand mathematical proofs;
(v) To communicate using mathematical language, written and orally.
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Syllabus |
Introduction - Examples and classification of DE.
ODE - Solution of a DE; IVP and BVP; Existence and uniqueness of the solution.
Scalar ODEs - Separable and homogeneous equations; Linear and Bernoulli equations; Exact and reducible to exact equations; Linear equations of order higher than 1; Method of undetermined coefficients; Method of variation of parameters.
Systems of linear ODEs - The solution space of linear systems; Matrix exponentials and Jordan canonical form; Solving systems of linear equations.
Notions of stability for autonomous equations - Orbit, phase portrait, and tangent field; Stability of equilibrium points; Flow and local behavior.
PDE - Definitions and classification; Boundary value problems; Second-order equations.
Separation of variables and Fourier method - Fourier series; Separation of variables; Fourier transform; Fourier method.
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Main Bibliography |
- Braun M (1993). Differential Equations and Their Applications. Springer
- Ross S (1984). Differential Equations. John Wiley and Sons
- Chicone C (2006). Ordinary Differential Equations with Applications, 2nd edition (Texts in Applied Mathematics, 34). Springer
- Doering CI e Lopes AO (2016). Equações Diferenciais Ordinárias, 6.a edição (Coleção Matemática Universitária). IMPA
- Hirsch MW, Smale S and Devaney RL (2013). Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd edition. Elsevier Inc.
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Language |
Portuguese. Tutorial support is available in English.
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