B029996 - MATHEMATICS WITH STATISTIC ELEMENTS FOR BIOLOGY

italian

Definitions, properties and examples of functions and sequences and their limits. Definitions, properties and examples of continuous functions. The derivatives of a function: definition, properties, calculations, applications. Definition of integral; methods of integrations. Differential equations. Mathematical models in dynamics of population. Calculus of probability and distribution of probabilities. Statistics.

For probability and statistics: M. Abate, Matematica e statistica. Le basi per le scienze della vita,
McGraw-Hill

For Calculus:
P.Marcellini- C.Sbordone, Elementi di calcolo, Liguori Editore .
P.Marcellini- C. Sbordone, Esercitazioni di Matematica, Liguori Editore,
Primo Volume

Calculus and applications to biology. Elementary probability and statistics.

Analysis of functions, integrals, solution of differential equations. Comprehension of a mathematical model. Solution of elementary problems in probability and statistics.

Understanding and analysing problems using rigorous mathematical tools.

Basic notions in mathematics and logic

lessons of theory and exercises,

Attendance at lessons is recommended.
The cours counts 96 hours.
Informations and materials is available on the e-learning page.
office hours by appointment

Written exam to test exercises skills (Problem solving ) and theoretical skils (statements fo definitions and theorems and their proofs with applications)

Real numbers, linear functions, polynomilas, rational functions, irrational functions. Exponential and logarithmic functions; trigonometric functions. Sequences and their properties. Limits of functions and of sequences. Continuous functions and their properties. Derivatives and applications. Integrals; defintion and calculus. Differential equations. Descriptive statistics: Frequency Tables and Graphs, sample mean, deviation, sample median, Sample Percentiles, sample mode, Sample Variance and Sample Standard Deviation, Sample Correlation Coefficient, linear regression, population and samples. Probability, Conditional Probability and Independence, Hardy-Weimberge law, application to genetic and to diagnostic test. Discrete and continuous Random Variables.

Complements:Evolution models in dynamics of populations and for diffusion processes. How to deduce the equation from the model. Central limit theorem and Tests Concerning the Mean of a Normal Population