- Docente: Enrico Bernardi
- Credits: 6
- SSD: MAT/05
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Quantitative Finance (cod. 8854)
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from Sep 16, 2024 to Oct 16, 2024
Learning outcomes
At the end of the course the student has comprehensive, in-depth coverage of the topics required in a one-term course in advanced calculus. The course is thought for students who have had a course in introductory algebra and undergraduate calculus. As for calculus, the student acquires a solid foundation in several variables calculus, vector analysis, linear algebra, systems of differential equations, vector fields, extremum problems. Furthermore, learns how advanced calculus can model and solve authentic real-world problems: thus tapping heavily into applied mathematics.
Course contents
Preliminaries
Topologies and Metric Spaces
Measuring Sets
The Lebesgue Integral
Measurable Functions
Spaces of Continuos Functions
Lebesgue Spaces
Absolute Continuity
Differential Equations
Elements of Complex Analysis
Elements of Fourier Analysis
Elements of Linear Algebra
Elements of Functional Analysis
Readings/Bibliography
Recommended text:
Principles of mathematical analysis
Walter Rudin
https://www.amazon.it/Principles-mathematical-analysis-Walter-Rudin/dp/0070856133/ref=sr_1_1?__mk_it_IT=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=3PQEAZ72KO870&dib=eyJ2IjoiMSJ9.P8-5ab0KEHtKqxeNlWIxRS3E8jucv8GyZ_Px2AVjxCNe6iFeeVYW81pqwHw3NyjsWtQEOvygn1LBqQYEA2rKfYeHeMezBnx3FYkuW3ug7nbBKLkPA5d7xZ_10WGp8ZlVZO1nEJhAdi8RJS01RO0l-PpXn13D5_wPr7fqHWeCIvfy7NEzOvZRki2n-H3ZpzOe2vGQ2VhqBGGZCz2UPnVRi0hSBJHr3Jn3GdZaWdO9GRqJm0dVNJng8sJcEd0iNxtrjeKe8Kwc0e28AJiThDqSeLykT2R0rWIiHgD5T4V_xI4.b5EG3mZOhnluI74KiRZ4rZUA7xkuJI-Pp9yQRt65wZ8&dib_tag=se&keywords=walter+rudin&qid=1720096767&sprefix=walter+rudin%2Caps%2C125&sr=8-1
Teaching methods
Traditional black-board based classes and every lecture will be made available through online platforms.
Assessment methods
Written ( and optional oral ) exams. The written exam is articulated in a series of 6 exercises each with a maximum grade of 5 points. Every exercise attains to elements of the syllabus and the relevant Bibliography covered during the course lectures or otherwise hinted at during classes. The (optional ) oral exam may cover the same range of topics as well, while keeping into accont the candidate's perfomance in the previously held written test.
Some more details may be in order:
[1] Grades are expressed on a scale from 0 to 30 cum Laude (30L), where 18
is the passing threshold.
[2] It is highly recommended that students attend to classes, where a
number of exam-like problems will be solved and presented completely.
[3] Written exams may last from 1 to 3 hours,
depending on the stage and the session they are attached to. Written
exams are open books.
[4] Written exams will be mainly made up by a
collection of exercises, some of them basic run of the mill stuff,
some more challenging.
[5] The method of execution, the precision of
presentation and, needless to say, the correctness and the accuracy of
the results will constitute the main factor in establishing the grade.
[6] The optional oral exam will be graded in a similar manner and an
arithmetic mean of the (i.e. written and oral) grades will yield the
final mark.
Teaching tools
Supplementary notes and material may be suggested and handed out during the course.
Office hours
See the website of Enrico Bernardi
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.