75376 - Calculus

Learning outcomes

By the end of the course, the successful student has the ability to apply the methods of differential and integral calculus, to plot the graph of functions, and to find and classify critical points of functions of two variables.

Course contents

This course provides an introduction to the foundational concepts of calculus, focusing on differential and integral calculus of functions of one variable. Topics include limits and continuity, techniques of differentiation, applications of the derivative, the concept and computation of definite and indefinite integrals, and an introduction to differential equations.
The course emphasizes both the theoretical underpinnings of calculus and its applications to real-world problems, particularly in the natural sciences. Students will explore how calculus is used to model dynamic systems, including rates of change, motion under gravity, population growth.

Special focus will be given to:

Formulating and solving first-order differential equations that arise in physical contexts (e.g., Newton’s Law of Cooling, exponential decay, simple harmonic motion).

Understanding how derivatives describe motion, velocity, and acceleration in physics.

Applying integrals to compute area.

Students will develop strong problem-solving skills, mathematical reasoning, and the ability to connect calculus concepts with real-world scenarios.

Some notions of multivariable calculus will be given (gradient and Hessian)

Readings/Bibliography

Mathematical methods for applications, CEA Bisi, Fioresi

Teaching methods

Lectures in class.

Assessment methods

Written and oral test.

Teaching tools

virtuale.it

Office hours

See the website of Rita Fioresi

See the website of Mattia Vincenzo Edoardo Massone