Elements of Infinitesimal Analysis III

Cod: 21032

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

^{n}. Line and surface integrals.

Fubini, Green, divergence, and Stokes' theorems.

Applications to problems in electromagnetism and continuum mechanics.

2. Line and surface integrals

3. Fundamental theorems of integral calculus in R^n

(i) know the definition and the basic properties of the Riemann integral of real functions defined in R^{n} (linearity, Fubini's theorem, change of integration variables, the Fundamental Theorem);

(ii) know the definition, the basic properties, and be able to compute line integrals on sectionally C¹ paths; (iii) know the definition, basic properties and be able to compute surface integrals on orientable sectionally C¹ surfaces; (iv) know and know how to apply the classical theorems of vector analysis (Green, divergence, and Stokes theorems) to problems in Electromagnetism and Continuum Mechanics.

^{n}

2. Line integrals

3. Surface integrals

4. Classical theorems of vector analysis

5. Applications of the classical theorems to Electromagnetism and Continuum Mechanics

**Main Bibliography:**

Gabriel E. Pires; *Cálculo Diferencial e Integral em R ^{n}*, Coleção Ensino da Ciência e da Tecnologia, vol. 45, IST Press, Lisboa, 2012

[1] João Palhoto Matos,

[2] Gabriel Pires e Departamento de Matemática do IST,

[3] B. Demidovich et al.;

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