99739 - Elements of Mathematics

Learning outcomes

After having attended the whole Maths class, students master: - the basic elements of the mathematical body of knowledge; - mathematical procedures useful for subsequent classes. More specifically, students know: 1. standard algebric procedures for solving inequalities; 2. the essential features of elementary functions and geometrical transformations; 3. the main procedures of differential calculus; 4. basic elements of statistics and probability.

Course contents

Main Contents

Numbers classification: the sets N, Z, Q, and R's essential features and cardinality. Infinite - countable (denumerable) and uncountable - sets, and their cardinalities.

Discrete mathematics: factorials, permutations (with and without repetition), and combinations.

Binomial coefficients and Pascal's triangle.

Basic probability: Bernoulli's formula for binomial events.

Infinite geometric series: convergence criterion, and sums.

Continuous mathematics: domains, ranges, and graphs of elementary functions.

Bounded and unbounded functions, even and odd functions, injectivity.

Geometric transformations on functions: symmetries and translations.

Basic equations and inequalities of different kinds: irrational, with absolute value, exponential, and logarithmic.

Mathematical analysis: accumulation points, limits of functions, and indeterminate forms. Asymptotic equivalence and asymptotes.

Continuity and derivability: derivatives of elementary functions, and applications (tangent line to a curve).

Plan of function investigation, convexity and inflexion points included.

Basic algorithms for the computation of primitive functions.

Definite integrals: Newton-Leibniz formula for continuous functions.

Introduction to differential equations.

Element of statistic and Probability

Readings/Bibliography

PDF slides  

for those who want to go into details:

"Metodi matematici per le scienze applicate" Bisi, Fioresi

edito da Taylor and Francis

English and italian versions available.

Teaching methods

Recurring sequences of lectures and exercises

Assessment methods

Exam

The exam lasts 2 hours, and consists of a hierarchical series of exercises.

The first part deals with the most elementary items of the main contents: it allows students to get a passing grade. The second part allows students to get higher marks

Teaching tools

frontal lessons - pdf notes on theory and exercises

Office hours

See the website of Robin Vanzolini