﻿ Mathematical Analysis II - Construção e ReabilitaçãoInstituto Politécnico de Tomar

# IPT

Ano Letivo: 2016/17

# 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 (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 the skills required to work with differential and integral calculus in functions of several real variables.

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: two written tests.
Exam assessment: one written test.

Bibliography
- Silva, J. (1999). PrincÃ­pios de AnÃ¡lise MatemÃ¡tica Aplicada. (pp. 1-472). Lisboa: : McGraw-Hill
- 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 proposed subjects. Theoretical-practical lectures in which exercises are proposed and solved.

Software used in class