- Docente: Stefano Bordoni
- Credits: 5
- SSD: MAT/05
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Rimini
- Corso: Single cycle degree programme (LMCU) in Pharmacy (cod. 9078)
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.
Further Contents (to get full marks)
Inverse functions.
Riemann’s improper integrals.
Solving inequalities graphically.
To get full marks “with honour”
Prove that 0! = 1.
Prove that Q is denumerable.
Prove that √2 is not rational.
Prove that there are infinitely many prime numbers.
Prove that R is uncountable.
Prove Torricelli-Barrow-Newton’s theorem.
Readings/Bibliography
Warner & Costenoble, FINITE MATHEMATICS AND APPLIED CALCULUS, Brooks/Cole, 2017 (OR other editions - some copies available in the university library)
Teaching methods
Recurring sequences of short 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
Brief handouts dealing with theoretical memos and exercises
Office hours
See the website of Stefano Bordoni