Mathematical Analysis II

Recommended Prerequisites

Mathematical Analysis I. 

Teaching Methods

The teaching methods in the theoretical components will be predominantly expository and should include examples. In the practical components problems will be solved under the guidance of the teacher. The independent resolution of problems must be encouraged. As much as possible examples and exercises from the field of Electric and Computer Science Engineering.

The interaction between concepts and their practical application must be discussed, giving a central role in the visualization and analysis of particular situations before making a progressive abstraction of the concepts being introduced

Learning Outcomes

The main goal of the course is to introduce the basic tools from Differential and Integral Calculus for functions of several real variables, including the basic concepts for studying curves and surfaces in the plane and in the tridimensional space. The relevance of the results presented in terms of the applications should be emphasized. It is also intended that students acquire a knowledge of the concepts in order to assess the scope and limitations of the materials studied and their applications.

The course aims at developing the following skills: analysis and synthesis, organization and planning, oral and written communication, problem-solving skills and computational ability. On the personal level it also allows to develop self-learning skills and independent thinking. 

Work Placement(s)

No

Syllabus

Real functions of several real variables – differential calculus

· Limits and Continuity

· Partial Derivatives

· Differentiability

· The Chain Rule

· Directional Derivatives and the Gradient Vector

· Implicit function theorem

· Maximum and Minimum Values. Lagrange Multipliers.

Curves Defined by Parametric Equations and Polar Coordinates

Integral calculus over R2 and R3

· Double Integrals and Applications

· Triple Integrals and Applications

· Change of Variables in Multiple Integrals (including polar, cylindrical, and spherical coordinates)

· Line Integrals. Green’s Theorem

· Surface Integrals. Stokes and Divergence Theorems.   

Head Lecturer(s)

Susana Margarida Pereira da Silva Domingues de Moura

Assessment Methods

Assessment 2
Resolution Problems: 50.0%
Mini Tests: 50.0%

Assessment 3
Exam: 100.0%

Assessment 1
Frequency: 100.0%

Bibliography

• Stewart, J. (2006) – Cálculo, Volumes II, 6ª ed., Pioneira Thomson Learning, São Paulo.

• Breda, A., Costa, J (1996) – Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa.

• Carvalho e Silva, J. (1994) – Princípios de Análise Matemática Aplicada, McGraw-Hill, Lisboa.