Mathematical Analysis III

Recommended Prerequisites

N.A.

Teaching Methods

The theoretical lectures are predominantly expository. In practical classes the students will solve exercises under the guidance of the instructor. The students will also be encouraged to solve problems independently. In the theoretical classes it will prevail a strong interaction between concepts and their practical application, giving, as much as possible, a central role to visualization and analysis of particular situations before making a progressive approach to more abstract notions.

Learning Outcomes

Provide knowledge about integral calculus of real-valued functions of two and three variables, ordinary differential equations and systems of linear differential equations, as well as the fundamental concepts about special function transforms relevant to applications to engineering and other sciences. Throughout the course, students must develop computational skills and acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the studied materials, as well as their applications.

Work Placement(s)

No

Syllabus

Integral calculus in R2 and R3
• Double integrals and applications
• Triple integrals and applications
• Change of variables in double and triple integrals
• Line integrals. Green’s Theorem.
• Surface integrals. Stokes’ and Divergence Theorems.
Linear differential equations of order higher than one
• Solving homogeneous linear equations
• Method of the annihilator polynomial
• Reduction of order
• Method of variation of parameters
Systems of linear differential equations with constant coefficients
Laplace transform and applications in solving differential equations
Fourier transform.

Head Lecturer(s)

Amílcar José Pinto Lopes Branquinho

Assessment Methods

Evaluation
Exam: 100.0%

Bibliography

J. Stewart, Cálculo , 4ª ed., Vol.2, Pioneira, São Paulo, 2001.
A. Breda e J. Costa, Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa, 1996.
Dennis G. Zill, A first course in differential equations with applications, Brooks/Cole, 2005.