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The course

How to use this website

The website contains the lecture notes of the Mathematical Analysis 1 course, divided into five parts as in the PDF: numbers and logic, functions, limits (of sequences and of functions), derivatives, series. Each chapter can be read from beginning to end, or you can jump directly to a section from the menu on the right.

  • The colored boxes have the same color and number as in the PDF: definitions, theorems, worked examples, key points.
  • Proofs are folded: they open with a click.
  • The PDF of each chapter can be downloaded from the link at the top of the page; there is also a single PDF with all the lecture notes.
  • Search (at the top) finds words and formulas across all the notes.
  • Light or dark theme: with the icon at the top right.
  • On a phone the website reads well: long formulas scroll horizontally.

How to study

  1. Read the chapter with the definitions and statements; redo the examples by hand, with pen and paper, before looking at the solution.
  2. Use the interactive graphs to get a feeling for what a theorem says or how a function changes.
  3. Review the exam theorems: statement, hypotheses, proof.

Reference books

For those who want to go deeper or look for more exercises:

  • M. Bramanti, C. D. Pagani, S. Salsa, Analisi matematica 1, Zanichelli.
  • P. Marcellini, C. Sbordone, Analisi Matematica uno, Liguori.
  • M. Bramanti, Esercitazioni di Analisi matematica 1, Esculapio.
  • P. Marcellini, C. Sbordone, Esercitazioni di Matematica, vol. 1, Liguori.

Author

The lecture notes are by Fabio Furini; the exercises with solutions by Fabio Furini and Gianluca Priori.

License

Text and figures are released under the CC BY 4.0 license: they can be used and shared with attribution. The code (interactive graphs, scripts) is released under the MIT license.