﻿ Mathematical Analysis II - Construção e ReabilitaçãoInstituto Politécnico de Tomar

# Construção e Reabilitação

## Mathematical Analysis II

Publication in the Diário da República: Despacho nº 9398/2015 - 18/08/2015

6 ECTS; 1º Ano, 2º Semestre, 30,0 T + 45,0 TP , Cód. 81067.

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.
Some applications of double integrals.
Triple integrals:
Definition and properties.
Triple integrals in cylindrical and spherical coordinates.
Some applications of triple integrals.

Evaluation Methodology
Continuous assessment: three written tests marked from 0 to 10. A minimum mark of 2 in each test and an overall mark of 10 exempts students from exam.

Exam-based assessment: an exam (worth 0-20) or resit covering all the material taught. Minimum pass mark:10

NOTES:

In any form of assessment, a mark of 15 or higher requires the student to take an extraordinary exam.

Bibliography
- Howard, A. (2000). Cálculo um novo horizonte. (Vol. II). London: Bookman
- Silva, J. (1999). PrincÃ­pios de AnÃ¡lise MatemÃ¡tica Aplicada. (pp. 1-472). Lisboa: : McGraw-Hill
- Stewart , J. (2013). Introduction to calculus and analysis . (Vol. II). São Paulo: São Paulo: Cengage Learning
- Swokowsi, E. (1995). CÃ¡lculo com Geometria AnalÃ­tica. SÃ£o Paulo: Makron Books
- Zill, D. e Cullen, M. (2009). Advanced Engineering Mathematics. (Vol. 1). Sudbury: Jones & Bartlett Publishers

Teaching Method
Theoretical lectures with presentation and illustration of the subject content. Theoretical-practical classes involving problem-solving.

Software used in class
Not applicable