ID:
500121
Duration (hours):
83
CFU:
9
SSD:
ANALISI MATEMATICA
Year:
2025
Overview
Date/time interval
Secondo Semestre (02/03/2026 - 12/06/2026)
Syllabus
Course Objectives
The course will provide a comprehensive knowledge of differential and integral calculus for real and vector-valued multivariable functions, and some notions on power series. Priority will be given to the understanding and the ability of applying the definitions and the main results, rather than focusing on the proofs (however, some of them will be discussed in detail). A large number of examples and exercises will be provided: at the end of the course students will be proficient in the main theoretical notions and will be able to make computations involving power series, directional and partial derivatives, multivariable integrals, line and surface integrals.
Course Prerequisites
Calculus I, Geometry and Linear Algebra.
Teaching Methods
Lectures given by the teachers of the course. A significant part of the lectures will be devoted to examples and exercises. Attending the lectures is strongly recommended.
Assessment Methods
The exam consists of a written test. The exam time is at most 3 hours. In the test students will be asked to solve some exercises and to answer some theoretical questions. During the exam books, notes, calculators are not allowed. The exam is passed if the final score is greater than or equal to 18/30. The results of the test will be communicated by email. An oral exam may be required by the exam committee in some cases.
Texts
M. Bramanti, C.D. Pagani, S. Salsa. Analisi Matematica 2. Zanichelli, Bologna, 2009.
S. Salsa, A. Squellati. Esercizi di Analisi Matematica 2. Zanichelli, Bologna, 2011.
S. Salsa, A. Squellati. Esercizi di Analisi Matematica 2. Zanichelli, Bologna, 2011.
Contents
• Multivariable differential calculus. Main topological notions in R^n. Limits and continuity. Partial derivatives, directional derivatives, gradient. Higher order derivatives. Differentiability. Optimization with and without constraints.
• Multiple integrals. Integrals in two and three dimensions: definition and main properties; applications to Geometry and Physics. Integral calculus: reduction formulas; change of variables.
• Line integrals and surface integrals. Curves in a parametric form. Rectifiable curves and arc-length. Surfaces in a parametric form. Area of a surface; rotation surfaces. Line integrals with respect to the arc-length. Line integrals of vector-fields and applications to Physics. Surface integrals and applications to Physics. The divergence and the curl operators.
• Conservative fields. Green Theorem in R^2. Stokes Theorem and divergence theorem in R^3.
• Multiple integrals. Integrals in two and three dimensions: definition and main properties; applications to Geometry and Physics. Integral calculus: reduction formulas; change of variables.
• Line integrals and surface integrals. Curves in a parametric form. Rectifiable curves and arc-length. Surfaces in a parametric form. Area of a surface; rotation surfaces. Line integrals with respect to the arc-length. Line integrals of vector-fields and applications to Physics. Surface integrals and applications to Physics. The divergence and the curl operators.
• Conservative fields. Green Theorem in R^2. Stokes Theorem and divergence theorem in R^3.
Course Language
Italian
More information
Students belonging to one of the groups identified by the innovative teaching project may request to have access to the teacher's lecture notes and to schedule office hours also in an online format and by appointment, at times to be agreed upon with the teacher.
Degrees
Degrees
ELECTRONIC AND COMPUTER ENGINEERING
Bachelor’s Degree
3 years
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People
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