MATHEMATICS AND EXERCISES-1

The course belongs to the core educational activities on Mathematics, Physics and Statistics. The Course aims to provide the students with theoretical and applied fundamentals about differential and integral 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,
- methods for solving definite and indefinite integrals.

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;
- for solving indefinite and definite integrals of function of one variable.

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.
Integral definition and properties.
Fundamental theorem of calculus.
Anti-derivatives.
Integration by parts and by substitution.

- 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 .

Examination Module 2: it consists of a written test (duration: two hours) with open-ended problems aimed at verification of all the course contents in order to evaluate the ability of students in solving problems about applied calculus, computing limits, derivatives and integrals, and analysing the graph of a function. No mid-term exams are planned. During the written test, the students are allowed to consult theory notes. The grade is given by the sum of the scores assigned to the single problems: some problem consists of some questions whose score is proportional to the intrinsic difficulty. The exam will be passed if and only if the minimum grade is 18. In the moodle page of the course, some written tests of the previous years will be posted.

Indications for the final grade.
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 Calculus is the average of the grades of the two modules, with approximation by excess. The maximum grade of Calculus, 30 summa cum laude, is assigned with the full agreement of both the teachers only. The grade of the first module is valid until the second module is passed: however, students are strongly advised to pass both modules in the same academic year.

written

Assessment grid:

A. range 18-22
- sufficient knowledge and understanding of the program;

B. range 23-26
- fair knowledge and understanding of the program;
- fair rigor in conducting the exercises;

C. range 27-30
- good knowledge and understanding of the program,
- good rigor in conducting the exercises;

D. honors will be awarded in the presence of excellent knowledge and understanding of the program.

-Front lectures;
- Exercise sessions in class;