- Docente: Laura Galli
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Architecture-Engineering (cod. 5695)
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from Sep 16, 2024 to Dec 09, 2024
Learning outcomes
At the end of the module, the student is expected to be familiar with the fundamental tools of linear algebra and multivariate calculus.
Course contents
- Elements of Linear Algebra — Definition of vector spaces, linear dependence and independence, basis. Matrices: operations on matrices. Square matrices: trace, inverse, determinant. Systems of linear equations and the Gauss-Jordan method; rank and the Rouché-Capelli theorem; Cramer's formula. Linear mappings and endomorphisms: diagonalizability and characteristic polynomial. Affine spaces, plane and space geometry.
- Multivariable Calculus — Functions of several real variables with scalar or vector values. Continuity, differentiability, partial derivatives. Gradient, Jacobian matrix, Hessian matrix. Taylor's formula for real functions of several real variables. Maxima and minima of differentiable functions. Multiple integrals and Fubini reduction theorem. Change of variables. Overview of curves in R^n, line integrals and their applications.
Readings/Bibliography
- Marco Bramanti Carlo Domenico Pagani Sandro Salsa
Analisi matematica 2 (2009)
- Sandro Salsa Annamaria Squellati
Esercizi di Analisi matematica volume 2 (2011)
Teaching methods
- Lectures.
Assessment methods
The assessment consists of a written exam of 2 hours.
Teaching tools
Additional materials will be available on the course "Virtuale" page.
Office hours
See the website of Laura Galli