B5859 - ELEMENTI DI MATEMATICA

Learning outcomes

At the end of the course, the student will:

• Have knowledge of fundamental mathematical notions and their main applications within the biological and health sectors.

• Be equipped with the competencies required for the autonomous application of mathematical instruments in professional practice.

Course contents

Review of Elementary Functions

• Concept of function and main examples in applied sciences
• Linear, polynomial, rational, and algebraic functions
• Exponential and logarithmic functions, with applications to Malthus’ laws
• Elementary trigonometric functions

Limits and Continuous Functions

• Definition of limit and fundamental properties
• Notable limits, infinities, and infinitesimals
• Continuity of functions and limit theorems
• Derivatives of elementary functions
• L’Hôpital’s rule

Differentiable Functions and Function Analysis

• Derivative as rate of change and linearization
• Relationship between differentiability and continuity
• Maxima and minima, optimization problems
• Complete function analysis with practical applications
• Theorems of differential calculus

Definite and Indefinite Integrals

• Definition and properties of definite and indefinite integrals
• Fundamental Theorem of Calculus
• Integration techniques: substitution, integration by parts, rational and trigonometric functions
• Applications of integrals (areas, physical problems)

First-Order Differential Equations and Applications

• Definition and classification of first-order equations
• Cauchy problem and direction fields
• Separable and linear equations
• Applications: Newton’s law of cooling, mixing problems, growth models (Malthus)
• Autonomous equations: equilibrium and stability

 

The main theorems related to these topics will be presented, and exercises aimed at fostering the understanding of the theoretical concepts covered will be solved in class.

Readings/Bibliography

Metodi matematici per le scienze applicate, CEA Bisi, Fioresi

Esercizi risolti per Metodi matematici per le scienze applicate, CEA Bellisardi-Bisi-Fioresi.

For further study: Matematica. Calcolo infinitesimale e algebra lineare, Zanichelli, Bramanti-Pagani-Salsa.

 

Teaching methods

In presence lectures. At the end of each lecture, the materials used during the session will be uploaded to Virtuale. Each week, exercises drawn from the adopted textbook will be assigned for students to solve.

Assessment methods

The final examination will consist of a written test of three hours’ duration. Candidates will be required to solve exercises comparable to those assigned during the course and to answer a set of theoretical questions. The written test may be followed by an optional oral examination.

Teaching tools

The lecture materials will be uploaded to Virtuale in PDF format promptly after each class. Weekly exercises on the topics covered will also be assigned to support the students’ learning process. Tutoring sessions will be organized to review the material presented during lectures, and the instructor will be available for weekly office hours to answer students’ questions.

Office hours

See the website of Ferdinando Zanchetta