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Mathematical Analysis II

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Publication in the Diário da República: Despacho n.º 8644/2020 - 08/09/2020

6 ECTS; 1º Ano, 2º Semestre, 70,0 TP , Cód. 91196.

Lecturer
- Maria Cristina Oliveira da Costa (1)(2)

(1) Docente Responsável
(2) Docente que lecciona

Prerequisites
Not applicable

Objectives
a) To provide the mathematical foundations required in other modules of the programme.
b) To provide students with skills to use concepts and methods related to numerical series and functions, as well as the differential and integral calculation of real functions of several real variables.
c) To develop skills for analysis, calculation and deductive reasoning; as well as capacity for reflection and critical reasoning.

Program
CHAPTER I - Numerical and Function Series
Numerical series: definition and main properties.
Series of constant signal terms.
Absolute convergent and simply convergent series.
Operations with numeric series.
Function series.
Development of functions in power series.
Operations with development in power series

CHAPTER II - Real functions of several real variables
Introduction.
Limits and continuities.
Partial derivatives.
Differentiability.
Derivatives of composite functions.
Differentials of composite functions.
Derivation of implicitly defined functions.
Directional derivatives.
Homogeneous functions.
Local extremes.
Conditioned extremes.

CHAPTER III - Multiple Integrals
Double integrals:
Definition and properties.
Geometric interpretation of double integral as the volume of a solid
Double integrals in polar coordinates.
Applications of double integrals.
Triple integrals:
Definition and properties.
Triple integrals in cylindrical and spherical coordinates.
Applications of triple integrals.

Evaluation Methodology
The continuous assessment consists of three written tests. The first is rated from 0 to 6 values and following two tests are rated from 0 to 7 values. The student is passed by frequency if he obtains a grade of 10 or more, resulting from the sum of the three tests and at least 2 values on each test.

Bibliography
(1995). Cálculo Diferencial e Integral em R e Rn. (Vol. 1). (pp. 1-610). Lisboa: Mac Graw-Hill
(1995). Cálculo com Geometria Analítica. (Vol. 2). (pp. 1-744). São Paulo: Makron Books
(1999). Princípios de Análise Matemática Aplicada. (Vol. 1). (pp. 1-472). Lisboa: McGraw-Hill
(2000). Cálculo um novo horizonte. (Vol. II). London: Bookman
(2009). Advanced Engineering Mathematics. (Vol. 2). (pp. 1-1008). Sudbury: Jones & Bartlett Publishers
(2012). Introduction to calculus and analysis . (Vol. II). New York: Springer Science & Business Media.
(2013). Cálculo . (Vol. II). São Paulo: São Paulo: Cengage Learning.

Teaching Method
Theoretical-practical lectures, with presentation and illustration of the proposed subjects and also exercises are proposed to be solved.

Software used in class
Not applicable

 

 

 


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