Course - ISCAP

ECTS - Instituto Superior de Contabilidade e Administração do Porto
Degree: International Trade (evening Courses)
Course: Mathematics II
Academic Year: 2012/2013
Academic year: 1
Term: Summer Semester
Attendance: Mandatory
Number of Credits (ECTS): 5.0
Theoretical/Practical Work (hours): 3.0 h
Course Responsible Teacher: Mestre José Azevedo
Objectives:
1. To provide the students with the skills that are needed to succeed in the field of Management Sciences.
2. To guide the students in the learning process using an intuitive approach and illustrating the various topics with one or more
relevant application examples.
3. To encourage the students to use computational tools for solving some of the exercises.
Syllabus:
1- Integration
Indefinite Integrals
Antiderivatives
General Integration Rules
Techniques of Integration
Integration by Parts
Integration by Change of Variable
Integration of Rational Functions
Definite Integrals
Definition
Main Properties
The Fundamental Theorem of Calculus
Area between two Curves
Improper Integrals
Multiple Integrals
Partial Integration
Double Integration
Applications
2- Combinatorial Analysis
Introduction
Sample Space and Events
Counting Methods
Fundamental Counting Principle
Factorial Notation
Permutations
Combinations
Pascal#s Triangle. Newton#s Binomial Theorem.
3- Series
Definition
Convergence and Divergence
Geometrics, Mengoli and Riemann Series
Properties
Series of Positive Terms
Convergence Tests
Divergence Test
Comparison Test
The Ratio Test (D#Alembert)
The Root Test (Cauchy)
Applications
Objectives:
The theoretical and practical classes allow the students to be encouraged to learn by connecting theoretical results to a real
context. Slides, based on the adopted literature, are the main source used to teach the several topics and are supported by
examples and exercises.
Assessment Methods:
The students may select between (1) continuous evaluation # homework and two tests # and (2) final exam.
References:
António Carvalho Pedrosa, Sílvio Marques A. Gama, 2ª Edição, Porto Editora, 2007.
A. C. Pedrosa, M. L. Babo, A. P. Lopes, P. Ramos, C. Torres, Apontamentos de Matemática, ISCAP, Ano lectivo 2012/2013.
A. C. Pedrosa, J. Azevedo, M. L. Babo, J. Fonseca, A. P. Lopes, M. H. Loureiro, P. Ramos, C. Torres, Exercícios Propostos,
ISCAP, Ano lectivo 2012/2013.
A. C. Pedrosa, J. Azevedo, M. L. Babo, J. Fonseca, A. P. Lopes, M. H. Loureiro, P. Ramos, C. Torres, Exercícios Resolvidos,
ISCAP, Ano lectivo 2012/2013.
Howard Anton, Irl Bivens, Stephen Davis, Calculus, 10th Edition, John Wiley & Sons, 2012.
Ronald J. Harshbarger, James J. Reynolds, Matemática Aplicada: Administração, Economia e Ciências Sociais e Biológicas, 7ª
Edição, McGraw-Hill, 2006.
Ron Larson, Robert P. Hostetler, Bruce H. Edwards, Cálculo, Volumes 1 e 2, 8ª Edição, McGraw-Hill, 2006.
Mestre José Azevedo
S. Mamede Infesta, 13 de Março de 2013