Calculus

Course objectives

To give the fundamental concepts and tools of differential and integral calculus for functions from R to R, of numerical series and of complex numbers; to give some basic concepts and tools of differential and integral calculus in several real variables and of differential equations; to give an intuition, though examples and practical applications, of the use of Mathematical Analysis in the quantitative description of a phenomenon.Risultati di apprendimento attesi (Inglese):To read, understand and handle (e.g., represent graphically, approximate, rescale, calculate exactly) the mathematical objects introduced during the course (such as series, functions, integrals, gradients, differential equations). To know and understand their main properties.

Channel 1
FRANCISCO FACCHINEI Lecturers' profile
Channel 2
VALERIO DOSE Lecturers' profile

Program - Frequency - Exams

Course program
-Logic. Theorems and proofs. -The real numbers, bounded sets, sup, inf, completeness. -The complex numbers. -Real functions of one real variable. Standard functions (affine, quadratic, powers, exponentials, logarithmic, trigonometric): definition, properties and graph. -Limits of sequences and functions -Derivatives and the Taylor polynomial -Integrals -Series of numbers -Ordinary differential equations
Prerequisites
Basic set theory and algebra. First and second degree equations and inequalities. Rational equations and inequalities. Linear, quadratic, exponential, logarithmic, trigonometric, root functions, and equations and inequalities involving them.
Frequency
Not mandatory
Exam mode
Written test and possible oral test at the teacher's discretion
Lesson mode
Lectures and Exercise sessions in presence
  • Lesson code10606870
  • Academic year2025/2026
  • CourseManagement Engineering
  • CurriculumSingle curriculum
  • Year1st year
  • Semester1st semester
  • SSDMAT/09
  • CFU12