Calculus (unit 1)

AY 2020/2021

Applied Computer Science and Artificial Intelligence

Pagina MOODLE del corso


Final results for unit 1
The results are available HERE

Results of the written test Jan 8 2021 (Call 1)
The results are available HERE


This webpage is the main source of information for the course on Calculus (unit 1: Differential Calculus). Study materials and updates concerning the course will be published here first

Instructor

Piero D'Ancona (room 128, 1st floor, Istituto Castelnuovo)

When and where

Course Duration
Start: October 5, 2020
End: December 21, 2020

Class Schedule
Monday 8:00 - 11:00
Wednesday 11:00 - 13:00

Location
AULA BLU 3: it is building CU028 on this map

Office Hours
To be announced

Course Outline
A tentative outline can be found below, at the end of this page

Useful Links
InfoStud service. Registration on InfoStud is mandatory to take and validate an exam
ACSAI main page
Academic Year
Programme Calendart 2020-2021

Course Material

A complete set of notes covering all topics of the course is available (BEWARE: only Chapters 1,2,3 and 4 will be covered), together with additional material, sets of exercises and examples of past exams. Additional material (in italian, sorry):
FAQ: can you suggest other textbooks?
Answer: the topics of the course are standard and can be found in any basic treatise on Calculus. Notes and sets of exercises available on this page cover the needs of the course completely (and then some more). For students who want to go deeper, there are many excellent textbooks; a very good one is: Tom Apostol, Calculus, Volume I

Final Exam

The following instructions are tentative and they may change, pending the evolution of the pandemic

There will be 5 calls (Appelli) for the final exam, in January, February, June, July and September 2021. The exam is composed of a written test (mandatory) plus an oral test (optional). To take an exam, it is mandatory to register in the corresponding Appello via the InfoStud service

Written test. The written test is a two--page multiple choice test, see the examples above
  • Call I: January 8, 2021
  • Call II: January 25, 2021
  • Appello straordinario (reserved)
  • Call III: 22 June 2021
  • Call IV: 6 July 2021
  • Call V: 9 September 2021
  • Appello straordinario (reserved)
Oral test. The oral test is optional and takes place immediately after the written test or in the following days. Question will touch all topics of the course, including exercises

Course outline

The following outline is subject to change, due to the special circumstances

  • Week 1: 5-7 October
    • Real numbers. Powers and modulus of real numbers.
  • Week 2: 12-14 October
    • Equations, inequalities, systems. Sign and maximal domain of an expression
  • Week 3: 19-21 October
    • Max, min, sup, inf of sets. Functions of a real variable. Elementary functions: powers
  • Week 4: 26-28 October
    • Elementary functions: exponential functions, logarithms, trigonometric functions. Limits of functions
  • Week 5: 2-4 November
    • Properties of limits. Rules of calculus of limits
  • Week 6: 9-11 November
    • Exercises on limits of functions. Continuous functions
  • Week 7: 16-18 November
    • Sequences. Series
  • Week 8: 23-25 November
    • The derivative. The fundamental theorems of calculus.
  • Week 9: 30 November - 2 December
    • The graph of a function The Theorems of de l'Hopital.
  • Week 10: 7-9 December
    • The Taylor polynomial. Brief notions of multivariable calculus
  • Week 11: 14-16-21 December
    • Complex numbers. Exercises
  • Week 12: 21-23 December
    • Exercises