At the end of the course the student will master the main tools of mathematical analysis, useful for modeling phenomena in one and multiple variables. By the end of the course, students will understand the concepts of partial derivatives and gradients, as well as the concept of multiple integrals and the key properties of functions of multiple variables. They will be able to solve the main types of ordinary differential equations and utilize Fourier series to represent periodic functions. Additionally, students will be familiar with the concepts of Fourier transform and discrete Fourier transform.
Mathematical Analysis I. Some of the material within the course on Geometry and Linear Algebra will be helpful to take this course.
Lectures and practical activities.
The exam aims to verify the student's achievement of the educational objectives set by the course. In particular:
- mastery of the methods and techniques developed in the course
- awareness of their theoretical foundations
- adequacy of the language used.
The exam consists in a practical test (written) and a theoretical test (oral), both mandatory. The practical test is passed with at least 15 points out of 30. The students that pass the practical test may access the theoretical test.
Students can replace the practical test with two ongoing tests. The first ongoing test is held in the middle of the course, and concerns the first half of the program. The second concerns the second part of the program (including the prerequisites contained in the first part) and is held in conjunction with the first complete winter session written test.
The two ongoing tests have the same modality as the complete written test. The second test is accessed with a minimum score of 15 in the first test.
In the first winter session, the student who has passed the first ongoing test is free to decide whether to take the second ongoing test or the complete test.
The theoretical test is held 7/10 days after the practical test. Only in the exam sessions of january and june the student may postpone the theoretical test to february and july, respectively.
- Elements of differential and integral calculus for functions in several variables.
- First order and higher order differential equations
- Sequences and series of functions
- Fourier series
- Fourier transform
- Discrete Fourier transform
