27993 - Mathematical Analysis T-2

Course Unit Page

  • Teacher Carlo Ravaglia

  • Learning modules Carlo Ravaglia (Modulo 1)
    Carlo Ravaglia (Modulo 2)

  • Credits 6

  • SSD MAT/05

  • Language Italian

Academic Year 2015/2016

Learning outcomes

Refine and enrich the basic mathematical tools (series, curves, various types of integral, differential equations) in order to solve typical applicative problems.

Course contents

  1. Directional derivatives; partial derivatives; local bounds and gradient; differentiability.
  2. Linear differential forms.
  3. Implicit functions.
  4. Differential manifolds; Lagrange multipliers.
  5. Differential equations.
  6. Linear differential equations.
  7. Riemann integral.
  8. Lebesgue integral (short account).
  9. Integrals on manifolds.
  10. Integrals of differential forms on directed manifolds


We propose the following texts:

1. Carlo Ravaglia : Corso di Analisi Matematica L-B, Edizioni Dupress (2011).
2. Carlo Ravaglia: Analisi Matematica II - Compiti d'esame, Edizioni Dupress (2011).

For a description of the tools
and for the place where they are found see

Teaching methods

Lessons and exercises in classroom. For each topic is reserved a fixed number of hours. The total hours of lessons and exercises are exactly 60, according the planned program

Assessment methods

The exam is written and is divided into two parts:
1.Test of exercises,
2.Test of theory.
The exercises test comprises a series of exercises of a task, the same or in different versions for all students. It aims to assess the skills achieved in solving problems in the context of the issues addressed. It is not consented to the use of books, notes, calculators and computer media. Each exercise has a score, for a total of 33 points. Who holds a vote greater than or equal to 12.5 and less than 14.5, he is admitted to a recovery test of exercises, which, if positive carries the vote to 14.5. To be admitted to the test of theory it is necessary to have obtained in the exercises test, including through the recovery test, at least 14.5.The exercise test gives for the final grade a score equal to the vote of the test exercises divided by 30 and multiplied by 26. The test exercises is valid only for the appeal.

The theory test comprises the iterative written answer to some questions of theory and to some simple exercise, from an individual card with questions randomly chosen. It aims to test the knowledge of the program. The theory test gives for the final grade a score from -26 to 9.

The final grade is the sum of points obtained in the exercises test and of points obtained in the theory test.

For more details see
http://people.ciram.unibo.it/~ravaglia/corsi/comune/modalita11.htm .

See also
for the dates of examinations.


Teaching tools

We propose the following didactic tools:

  1. Texts of examination exercises academic years 2013/14 and 2014/15.
  2. Examination exercises academic year 2014/15 (texts and solutions).
  3. Examination exercises present academic Year 2015/16, after the assignation (text and solutions).
  4. Carlo Ravaglia: Corso di Analisi Matematica 2 - Esercizi.
  5. Detailed contents with marks of importance of the topics.
  6. Questions on theory and immediate exercises.

For a description of the tools
and for the place where they are found see



Links to further information


Office hours

See the website of Carlo Ravaglia