27210 - Mathematical Analysis 1 (A-L)

Learning outcomes

By the end of the course, students will acquire basic notions of infinitesimal and integral calculus, developing both the habit of scientific reasoning and a sensitivity to the analysis of mathematical models, especially through the study of the asymptotic expansion of functions. They will also be able to perform a detailed study of functions of one variable, sequences, and series, both numerical and functional.

Course contents

Elements of set theory. Real numbers. Complex numbers. Basic elements of the theory of functions of one real variable. Differential calculus for functions of one real variable. Theory of integration of functions of one real variable in the sense of Riemann. Generalized integrals. THeory of numerical series. Sequences and series of functions. Some methods of resolution of ordinary differential equations. 

Readings/Bibliography

Notes of the teacher (in preparation). In alternative:

E. Lanconelli, "Lezioni di analisi matematica I2, Pitagora Editrice. 

Teaching methods

Frontal lessons.

Assessment methods

Final applied and theoretical exams. The applied exam includes: 1) two exercises, for a maximum score of ten points; 2) a test with four multiple-choice questions. Four solutions are given, only one of which is correct; a correct answer is worth three points, an unanswered question is worth zero points, and an incorrect answer is worth one point less. 3) The applied exam is passed if the overall score for both parts is at least 11 (out of a maximum of 22). A score lower than 11 requires the student to repeat the exam in a subsequent exam session. 4) If the applied exam is passed, the student is admitted to the theoretical exam, which consists of two questions, one written and one oral, followed by a discussion. The minimum score for the exam to be valid is 4 points, with a maximum of 12. The final exam score (given two valid exams) is the sum of the scores plus one, with honors awarded if it is above 30. If the total score is less than 18, the exam will still be considered failed and must be retaken. A failed exam has no effect on subsequent attempts.

Teaching tools

Tutoring lessons (with a "tutor" appointed by the University).

Office hours

See the website of Davide Guidetti

See the website of Giovanni Eugenio Comi