- 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
Classification of numbers: the sets N, Q, and R, their essential features, and their cardinality. Numerically equivalent sets. Countably and uncountably infinite sets.
Permutations, dispositions (with and without repetition), and combinations.
Equations and inequalities of different kinds: irrational, with absolute value, exponential, and logarithmic.
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.
Mathematical analysis: some remarkable limits and indeterminate forms. Asymptotes.
Continuity and derivability: derivatives of elementary functions and applications.
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)
Basic probability: binomial probability formula for Bernoulli trials.
Inverse functions.
Riemann’s improper integrals.
The sum of infinite series: geometric series.
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 the set of primes does not have maximum.
Prove that R is denumerable.
Prove that .
Prove that the derivative of y = √x by solving an indeterminate form.
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