Mathematics and Physics

Introductory topics: physical quantities and units; order of magnitude; significant figures. Scalar and vector quantities; sum of vectors; scalar and vector product; representation of a vector by its coordinates.

Kinematics: average and istantaneous velocity; average and istantaneous acceleration; rectilinear motion at constant velocity and constant acceleration; circular motion at constant speed; parabolic motion; harmonic motion.

Dynamics of a material point: Newton's laws with applications; gravity; elastic force; vincular reactions; friction; a brief overview of the dynamics of continuum bodies and systems of several bodies; momentum; center of mass; torque; law of the lever.

Work and energy: definition of work; kinetic energy theorem; conservative forces; stable and unstable equilibria; mechanical energy conservation with applications.

States of matter: a brief overview of intermolecular forces; a qualitative descripion of gas, liquid, and solid states.

Statics and dynamics of liquids: pressure; Pascal's law; Stevin's law; Archimedes' law; flow rate; Bernoulli's theorem with applications.

Thermodynamics: internal energy; heat; temperature; modes of heat transfer; thermal capacity; equation of state of an ideal gas; expansion and compression work; first and second principles of thermodynamics; thermodynamic cycles, Carnot cycles, Carnot's theorem, a cusory glance at entropy.

Electricity: electric charge; Coulomb's law; electric field generated by a point charge, uniform electric field, electric potential;electric field flow, Gauss theorem, electric current; resistance; Ohm's law,law at the nodes, Kirchhoff's law.

Didactics
Significant figures, scientific notation, rounding numbers (1 hour)
Percents, ratios, fractions, proportions (1 hour)
Linear and quadratic equations (2 hours)
Systems of linear equations (1 our)
Functions, derivatives and graphic representation (1 hour)
Populations and samples. Type of statistic variables. Absolute and relative frequencies. Frequency distributions (3 hours)
Descriptive statistics: Mean. Median. Mode. Measures of dispersion: deviance, variance, standard deviation, coefficient of variation, range (2 hours)
Probability. Probability distributions (2 hours)
Comparing proportions. Binomial distribution. Poisson distribution (2 hours).
Normal distribution: Standardized variable (z), standard normal distribution table,. Asimmetry and kurtosis (3 hours)
Sampling distribution of a mean. The confidence interval of a mean. The sampling distribution of a proportion. Student's t-distribution. Comparison between two means (4 hours)
Hypothesis testing: Type I and TYPE II errors (2 hours)
The Chi-squared test. Contingency tables (2 hours)
Covariance. Correlation. Linear regression. (3 hours)
Analysis of variance (ANOVA): partioning of total sum of squares. The F-test. (2 hours)
Practice
- mathematics (2 hours)
- descriptive statistics (2 hours)
- normal distribution (2 hours)
- correlation and regression (2 hours)
- analysis of variance (2 hours)
- sampling distribution (3 hours)
- proportion, Chi-squared test (3 hours)