FUNDAMENTALS OF MATHEMATICS
Learning outcomes of the course unit
The purpose of the course is to explain basic concepts of Mathematical Analysis and supply a number of fundamental calculation techniques.
Prerequisites
Introduction : numerical and algebraic calculus; powers and logarithms: properties and calculation. Equations, inequalities and systems. Elements of analytical geometry; straight lines and conics.
The functions: basic concepts and analysis of the properties of elementary functions (powers, exponentials, logarithms, trigonometric functions) and graphic representation.
Limits and derivatives: definitions, limits and derivatives of elementary functions and rules of calculation. Study of function: increase and decrease, maxima and minima, concavity and convexity, asymptotes and graph.
Integrals: definition of indefinite integral with examples and definite integral and its geometric significance.
Course contents summary
Introduction : numerical and algebraic calculus; powers and logarithms: properties and calculation. Equations, inequalities and systems. Elements of analytical geometry; straight lines and conics.
The functions: basic concepts and analysis of the properties of elementary functions (powers, exponentials, logarithms, trigonometric functions) and graphic representation.
Limits and derivatives: definitions, limits and derivatives of elementary functions and rules of calculation. Study of function: increase and decrease, maxima and minima, concavity and convexity, asymptotes and graph.
Integrals: definition of indefinite integral with examples and definite integral and its geometric significance.
Recommended readings
V. VILLANI: 'Matematica per discipline biomediche', McGraw-Hill, Libri Italia.
For exercises:
P. MARCELLINI, C. SBORDONE:'Esercitazioni di Matematica', I volume, parte prima e seconda, Liguori Editore.
Teaching methods
The teaching method is based on classroom lessons supplemented by numerous examples and exercises in which student participation is encouraged and requested.
The final examination consists of a written test which may be supplemented by an oral exam: the student must demonstrate that he has mastered the calculation techniques presented and understands the topics covered.
