- Docente: Gabriele Sicuro
- 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 Oct 03, 2023 to Dec 19, 2023
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, and to know the basic elements of the theory of differential equations.
Course contents
Introduction to Complex Numbers — The field of complex numbers. Algebraic operations on complex numbers, conjugate, modulus, argument of a complex number. Trigonometric representation, De Moivre's formula, nth roots of a complex number.
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. Continuous, conservative, closed vector fields. Necessary and sufficient conditions for a field to be conservative.
Readings/Bibliography
Lecture notes will be provided via Virtuale.
In addition, students interested in learning more about the material are encouraged to consult the following volumes:
Linear algebra
Gilbert Strang, Introduction to Linear Algebra, Wellesley - Cambridge Press.
Edoardo Sernesi, Geometria 1, Bollati Boringhieri.
Aristide Sanini, Elementi di geometria, Levrotto & Bella.
Calculus
Giuseppe Zwirner, Istituzioni di Matematiche - Parte 2, CEDAM.
Enrico Giusti, Analisi Matematica 2, Bollati Boringhieri.
Teaching methods
Blackboard lectures.
Assessment methods
The assessment consists of a written exam of 2 hours. If the mark is greater than 15/30, it is possible to take a complementary oral exam to receive a higher mark. The oral exam is necessary for passing the exam if the value of the written examination is lower than 18.
Links to further information
https://gsicuro.github.io/lectures/im2/
Office hours
See the website of Gabriele Sicuro