Mathematics II
Code
7399
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Rui Alberto Pimenta Rodrigues
Weekly hours
6
Teaching language
Português
Objectives
- Being able to apply Calculus and Statistics to solve problems.
Prerequisites
Matemática I
Subject matter
Differential calculus: applications
-functions of several variables: partial derivatives
-Linear regression
-Errors in measurements. Maximum error propagation: addition and multiplication.
-Linear aproximation to a function in the neighborhood of a point. Error propagation: general case .
Integral calculus
-Integral of a function on an interval. Mean value .
-Computing primitives and integrals. Primitivation by parts.
-Differential equations: separable variables. Initial value problems.
Introduction to probability and statistics
-Discrete and continous random variables.
-Mean , variance and standard deviation of a random variable.
-The Normal distribution
-Mean, variance and standard deviation from a sample.
-Mean, variance and standard deviation of a sum and a mean from random variables.
-Confidance interval for the mean of a normal population given a sample. t-student distribution.
-Confidance interval for the differences between two means.
-Significance tests.
-Proportion between two populations. Testing proportions.
-Bilateral and unilateral tests.
Bibliography
- ANTON, Howard; Bivens Irl; Davis Stephen - Cálculo vol I e II, 8ª edição, Bookman, 2007.
-
Bento, Murteira- Probabilidades e Estatistica volI e II, McGraw-Hill
- Spiegel, Murray- Estatistica, McGraw-Hill, 1984
Teaching method
Lectures are given using a multimedia projector. The students have previously access to lectures-notes and to pratical-notes.
Evaluation method
First year students must attend, at least, two thirds of the classes.
There are three mid-term tests.
And 1 final exames.
To have a final note superior to16 the student must be submitted to an extra test.