Mathematical Analysis III

Recommended Prerequisites

Mathematical Analysis I, Mathematical Analysis II; Linear Algebra

Teaching Methods

Exposition will be the predominant method of teaching in the classroom. The theoretical/practical classes will be used to solve problems under the guidance of the teacher. It will be encouraged the autonomous resolution of problems. A strong interaction between concepts and their practical application will prevail. A central role to the visualization and analysis of particular situations will be given as much as possible, before making a progressive abstraction of the concepts introduced. The transformation of concepts into working tools will be achieved by encouraging personal work.

Learning Outcomes

To provide basic knowledge about integral calculus e differential equations theory as well as fundamental tools to its application on Engineering problems.

Work Placement(s)

No

Syllabus

  I) Integral Calculus in R2 e R3: I1) Double integral and its applications I2) Triple integral and its applications I3) Change of coordinates in double and triple integral (including polar, cylindrical and spherical coordinates) I4) Curl integral. Green’s Theorem I5) Surface integral. Stokes’s Theorem and the Theorem of divergence.

 II) Linear differential equations with order greater  than 1.II1)The annihilator Method II 2) D’Alembert’s Method  II 3) The variation of constants Method

III)  Systems of differential equations with constant coefficients.

IV) Laplace’s transform (with application to differential equations and systems)

Fourier’s transform

Head Lecturer(s)

Ana Margarida Mascarenhas de Melo

Assessment Methods

Continuous assessment
2 frequencies: 100.0%

Final assessment
Exam: 100.0%

Bibliography

1) Ana Breda e Joana Nunes da Costa, Cálculo com Funções de Várias Varáveis, McGraw-Hill, 1996.

2) James Stewart, Cálculo II, 5ª ed., Pioneira, Thomson Learning, São Paulo, 2006.

3) Denis Zill, A first course in differential equations, Thomson Learning.