| Code |
14923
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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 |
None
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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 analysis and understand mathematical proofs
(v) To communicate using mathematical language, written and orally
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Syllabus |
1 Differential equations
1.1 Generalities and geometric interpretation
1.2 Differential equations with separable variables
1.3 Scalar linear differential equations
1.4 Exact differential equations
1.5 Differential equations of higher order
1.6 Method of undetermined coefficients
2 Linear differential equations
2.1 Linear differential equations in the plane
2.2 Exponential of matrices
2.3 Jordan canonical form
2.4 Flow of a linear differential equation
2.5 Non homogeneous linear differential equations
3 Non-linear differential equations in IRn
3.1 Flow of a non-linear differential equation
3.2 Existence and uniqueness of solution
3.3 Continuous dependence on initial conditions and parameters
3.4 Differentiability of the flow
3.5 Local stability
4 Partial differential equations
4.1 Linear equation and principle of superposition
4.2 Heat equation and Fourier method
4.3 Laplace equation
4.4 Wave equation and d’Alembert formula
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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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Teaching Methodologies and Assessment Criteria |
The classes will be theoretical-practical. The teacher presents the concepts and enunciates the results, demonstrating many of them. It also illustrates the theory with examples and applications. The student is encouraged to participate in classes, interacting with the teacher and sometimes solving exercises and problems. Autonomous work will be encouraged, mainly consisting of exercises, problem-solving and mathematical demonstrations.
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Language |
Portuguese. Tutorial support is available in English.
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