MATHEMATICS AND EXERCISES-1

The course belongs to the core educational activities on Mathematics, Physics and Statistics. The Course aims to provide students with theoretical and applied fundamentals about differential calculus. Particular focus is dedicated to mathematical models that are useful in life sciences applications

To be able to study a function of a real variable.

Knowledge and understanding
- limit computation;
- derivative computation;
- study of the first derivative of a function;
- study of the second derivative of a function.

Applying knowledge
- for the study of a function;
- for mathematical modeling of simple environmental phenomena;
- for finding domain and co-domain of a function;
- for finding minima, maxima, points of inflexion, asymptotes of a function.

Self assessment
Students evaluate their own work and learning progress through exercises.

Program of mathematics and geometry of secondary school.

Mathematical models and sciences.
Relations and functions.
Domain, codomain.
logarithmic and trigonometric functions.
Limits: theorems and calculation.
Continuity of elementary functions.
Geometrical and physical meaning of the derivative.
Derivative of composite and elementary functions.
Classical theorems of differential calculus.
Higher order derivatives.
Study of a function with graphical representation.
Minima, maxima, points of inflexion.
Approximating functions: Taylor and Mac Laurin series.

- Appunti per un corso di matematica. Luciano Battaia. Available online at: http://www.batmath.it/matematica/0-appunti_uni/corso-ve.pdf
- Paul's Online Notes. Available online at: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx .

The final exam will be in written form and consists of 4 problem: 1 problem on applied calculus, 1 problem of limits, 1 problem on derivatives, and 1 problem on the study of the graph of a function

Indications for the final grade of MATHEMATICS AND EXERCISES.
Only the students that already passed the exam of Module 1 can take the exam of Module 2. It is possible to take both the modules 1 and 2 in the same day, in this rigorous succession. The final grade of Mathematics and Exercises is the average of the grades of the two modules, with approximation by excess. The maximum grade, 30 summa cum laude, is assigned with the full agreement of both the teachers only. In any case, students must pass the exams of both modules in the same academic year. Otherwise, any passing grade achieved in Module 1 will be cancelled.

-Front lectures;
- Exercise sessions in class;

Italian

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