Mathematics II
Objectives
Elementary knowledge in agreement with the program.
General characterization
Code
7399
Credits
6.0
Responsible teacher
Manuel Messias Rocha de Jesus
Hours
Weekly - 6
Total - 104
Teaching language
Português
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (science area).
Bibliography
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ANTON, Howard; Bivens Irl; Davis Stephen - Cálculo vol I e II, 8ª edição, Bookman, 2007.
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Bento, Murteira- Probabilidades e Estatistica volI e II, McGraw-Hill.
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Spiegel, Murray- Estatistica, McGraw-Hill, 1984.
Teaching method
In theoretical sessions the contents of the course are exposed and illustrated with examples. In problem-solving sessions students will be asked to solve problems.
Any questions/doubts are clarified during classes or tutorial sessions or even in extra sessions combined directly between student and teacher.
Evaluation method
Students must attend, at least, 2/3 of problem-solving classes.
Each student will be evaluated by two tests or an exam. More details in the portuguese version.
Subject matter
Applications of differential calculus
-Functions of more than one variable: partial derivatives.
-Linear regression line of a set of points.
-Errors in measurements. Maximum error propagation: estimation. Addition and multiplication. Linear approximation of a function in the neighborhood of a point in the domain. Maximum error propagation: general case of a function of several variables.
Integral Calculus
-Notion of integral of a function in an interval. Average value of a function.
-Calculation of primitives and integrals. Primitive by parts.
-Differential equations of separable variables. Problems with initial conditions.
Introduction to probability and statistics
-Discrete and continuous random variables.
-Mean, variance and standard deviation of a random variable.
-The Normal distribution.
-Sample mean, variance and standard deviation.
-Mean, variance and standard deviation of the sum and mean of random variables.
-Confidence interval for the mean of a known normal population in a sample. t-student distribution.
- Significance tests for means.
-Proportion of two classes in a population. Test to compare proportions.
-Unilateral and bilateral tests.