Calculus II

Recommended Prerequisites

Calculus I

Teaching Methods

The theoretical lectures are predominantly expository. In practical classes the students will solve exercises under the guidance of the instructor. 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. The transformation of concepts into working tools will be achieved by encouraging personal work. The formal lectures will be complemented by periods of individual attendance.

Learning Outcomes

To provide students with basic knowledge of differential calculus of functions of several variables and with the fundamental concepts in the study of sequences and series. It is intended that the students acquire computational skills. It is also intended that the students acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the materials studied and their applications.

Work Placement(s)

No

Syllabus

Numeriacal sequences and series: Convergence criteria.

Sequences and series of functions: Uniform convergence. Power series: Taylor’s formula and Taylor’s series. Fourier series.

Real functions of several variables – Differential Calculus: Limit and continuity. Partial derivatives.

Differentiability. Derivatives of composition of functions. Directional derivatives. Gradient. Implicit

function Theorem. Maxima and minima. Lagrange multipliers.

Head Lecturer(s)

António José Esteves Leal Duarte

Assessment Methods

Continuous assessment
Continuous evaluation is done throughout the semester amd may consist of tests, quizzes or homework. The weight of each of these components for the final classification depends on the material under evaluation. Those students who obtain a grade higher or equal to 10 (out of 20): 100.0%

Final assessment
he final evaluation requires an exam quoted for 20. : 100.0%

Bibliography

Stewart, J. Cálculo , 4ª ed., Vol 1 e Vol.2 , Pioneira, São Paulo, 2001

Carvalho e Silva, J., Princípos de Análise Matemática Aplicada, McGraw-Hill,

Lisboa, 1994

Campos Ferreira, J., Introdução à Análise Matemática, Fund. Calouste Gulbkenkian,1993.

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

Spiegel, M., Análise de Fourier, Colecção Schaum, São Paulo, 1977.