[Gianluca
Gorni's home
page ]
Lecture Notes (in
Italian )
Video recording of a conference of mine (in Italian) on ancient geography, entitled "The island which is not there" .
YouTube video recording of a lecture : Spatial interaction and functional response in Lotka-Volterra prey-predator systems. By Elena Bozzetto, Gianluca Gorni. A graduation work in Mathematics at Udine University, Italy. Evento em homenagem aos 75 anos do Profº Ângelo Barone Netto. IME-USP, São Paulo, Brasil, 2011-08-01. An interdisciplinary topic: biology/ecology, differential equations, probability, special functions, computer stochastic simulation.
Registrazione YouTube di una lezione di Istituzioni di Analisi Superiore del 2021-04-16 all'Università di Udine, in cui si usano animazioni per far capire l'idea sottostante al Teorema delle infinite estrazioni di sottosuccessioni col metodo diagonale. Enunciato: se abbiamo una matrice reale a due indici $A_n(k)$, con $n,k\in\N$, tale che l'insieme $\{A_n(k): n\in\N\}$ sia limitato per ogni~$k\in\N$, allora esiste una $\varphi\colon\N\to\N$ strettamente crescente tale che la successione $n\mapsto x_{\varphi(n)}(k)$ converge per ogni~$k$ fissato. Il teorema schiude le applicazioni della compattezza a spazi a dimensione infinita.
YouTube playlist of three recorded lectures (in Italian) on a visual introduction to the functions of two variables.
VIDEO
Mathematica file . You can view it with the free Wolfram Player ).
Mathematica notebook (152MB)
YouTube playlist of two recorded lectures (in Italian) on a visual introduction to the concept of derivative of a function, based on the idea of zooming into the graph of the function.
VIDEO
Mathematica file . You can view it with the free Wolfram Player ). The two YouTube lectures separately: Lecture on YouTube, part 1 , Lecture on YouTube, part 2 .
YouTube playlist of three recorded lectures (in Italian) as an introduction to the concept of limit, based on animated decimal numbers and a soccer-like game.
VIDEO
Mathematica file . You can view it with the free Wolfram Player . The two YouTube lectures separately: Lecture on YouTube, part 1 , Lecture on YouTube, part 2 , Lecture on YouTube, part 3 . page.
YouTube video of a recorded lecture (in Italian) about the mean value theorems of Rolle, Lagrange and Cauchy .
VIDEO
YouTube playlist of two recorded lectures (in Italian) as an introduction to the integral of a function .
VIDEO
PDF file . Also: printable
text summary . The two YouTube lectures separately:
Lecture on YouTube, part 1 ,
Lecture on YouTube, part 2 .
YouTube playlist of twelve recorded lectures (in Italian) on an introduction to LaTeX, a system for writing mathematics by computer .
VIDEO
Lecture notes on Hilbert spaces and compact operators (2.7MB).
Using your fingers
to count in base 16 (42K).
The Greek
alphabet, for use in mathematics and computer science
(69K).
Cardano's solution to
the third degree equation (140K).
The induction
principle (100K)
Set theory
(229K).
Set-theoretic
relations (120K).
Peano's
axioms (153K).
Infinite
cardinalities (116K).
The square root of 2 (442K).
Uniform
continuity in dimension 1 (164K).
Iterating
functions of one variable (118K).
Some
"pathological" functions of one variable (188K).
Limit points of a
sequence of real numbers (104K).
The sequence of
the powers of a complex number (138K).
Some different ways of
making R^2 a normed space (89K).
Cantor's set and Peano's curve (237K). See also the companion Mathematica notebook and Peano's
curve QuickTime Movie (700K).
Van der Waerden's nowhere differentiable function (256K); see also the companion Mathematica notebook .
Some aspects of the
complex exponential function explained through pictures
(248K).
An elementary proof
of the fundamental theorem of Algebra (95K).
A pictorial introduction to functions of two variables (2.9 MB). Mathematica notebook (152MB)
Double integrals through pictures (16MB). You can view it with the free Wolfram CDF Player .
Some examples of integration in two variables (7MB) .
A videogame to illustrate the definition of limit (32K). You can view it with the free Wolfram CDF Player .
A summary of indeterminate limits, with final quiz (32K). You can view it with the free Wolfram CDF Player .
A tutorial on the mean value theorems by Rolle, Lagrange and Cauchy . You can view it with the free Wolfram CDF Player ). Lecture on YouTube
Animations to visualize real-valued functions on the unit circle , to set the stage for Fourier analysis. (You can view the cdf with the free Wolfram CDF Player )
Animations to visualize the complex powers on the unit circle
Pictures to illustrate trigonometric Fourier
series: pdf version (633K) and cdf version with animations (37M) .
The convolutions of functions explained with pictures .
Fourier approximants visualized as composition of uniform circular motions .
The Hahn-Banach theorem illustrated (290K) (You can view the cdf with the free Wolfram CDF Player )
Semiintegrable
and measurable functions (160K).
Illustrations on Taylor
polynomials in pdf format and in cdf format .
Construction of Lebesgue measure in Euclidean space .
Vitali-Lebesgue's theorem on the relation between Riemann and Lebesgue integration .
Lusin's theorem on the approximations of a measurable function with continuous functions .
The orthogonal projection onto the closed subspace generated by an orthonormal system in a Hilbert space .