- 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.

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. The two lectures are also available to Udine University members on the Microsoft streaming platform, free of advertisement. Take a look at the Analisi 1 page. - YouTube playlist of two recorded lectures (in Italian) as an introduction to the concept of limit, based on animated decimal numbers.

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. The two lectures are also available to Udine University members on the Microsoft streaming platform, free of advertisement. Take a look at the Analisi 1 page. - YouTube video of a recorded lecture (in Italian) about the mean value theorems of Rolle, Lagrange and Cauchy.

The lecture is also available to Udine University members on the Microsoft streaming platform, free of advertisement. Take a look at the Analisi 1 page. - YouTube playlist of two recorded lectures (in Italian) as an introduction to the integral of a function.

PDF file. Also: printable text summary. The two YouTube lectures separately: Lecture on YouTube, part 1, Lecture on YouTube, part 2. The two lectures are also available to Udine University members on the Microsoft streaming platform, free of advertisement. Take a look at the Analisi 1 page.

- YouTube playlist of twelve recorded lectures (in Italian) on an introduction to LaTeX, a system for writing mathematics by computer.

The twelve lectures are also available to Udine University members on the Microsoft streaming platform, free of advertisement. Have a look at the TeX page. - 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). See also a
java live 3D version of one of the graphs.
- 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.