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

Riemann integral in R^{n}. Line and surface integrals.

Fubini, Green, divergence, and Stokes' theorems.

Applications to problems in electromagnetism and continuum mechanics.

Fubini, Green, divergence, and Stokes' theorems.

Applications to problems in electromagnetism and continuum mechanics.

1. Multiple integrals

2. Line and surface integrals

3. Fundamental theorems of integral calculus in R^n

2. Line and surface integrals

3. Fundamental theorems of integral calculus in R^n

After concluding this course the student should be able to:

(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.

(i) know the definition and the basic properties of the Riemann integral of real functions defined in R

(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.

1. Riemann integral in R^{n}

2. Line integrals

3. Surface integrals

4. Classical theorems of vector analysis

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

2. Line integrals

3. Surface integrals

4. Classical theorems of vector analysis

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

Gabriel E. Pires;

[1] João Palhoto Matos,

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

[3] B. Demidovich et al.;

E-Learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).