MATHEMATICS AND EXERCISES-1

The course provides a single final grade and is divided into two modules, each with its own assessment test.
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.
The course contributes to the achievement of the program's educational objectives, particularly the development of mathematical skills for the analysis of environmental phenomena.

1. Knowledge and Understanding
1.1 Know the basic mathematical elements of the continuum and understand deductive reasoning.
1.2 Know the fundamental definitions of mathematical analysis for functions of one variable.
1.3 Know the main theorems of mathematical analysis for functions of one variable.

2. Ability to Apply Knowledge and Understanding
2.1 Know how to calculate the limits of functions.
2.2 Know how to calculate the derivatives of functions.
2.3 Know how to apply the fundamental elements of differential calculus to identify critical points.

3. Judgment
3.1 Know how to apply acquired knowledge to the expression of simple phenomena of interest to environmental sciences in terms of a mathematical model.
3.2 Know how to interpret the behavior of a function from its graph.
3.3 Know how to check the fidelity of the mathematical model to the constraints of a real-world problem.

4. Communication Skills
4.1 Ability to clearly and effectively communicate the results of a quantitative study, both in written and oral form.
4.2 Ability to interact with the instructor and other students during lectures and during exercises.

5. Learning Skills
5.1 Ability to take notes and interact with the instructor through active participation in lectures and exercises.
5.2 Ability to evaluate one's own progress in learning the subject matter at various stages through self-assessment tests.

Good theoretical and practical knowledge of high school algebra, geometry, and trigonometry. If you have any prior knowledge gaps, it's helpful to take the Basic Mathematics course.

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
- A large collection of various materials will be made available through the Moodle online teaching platform

Module 1 Exam: This consists of a written exam, lasting a maximum of two hours, with open-ended problems designed to test students' ability to calculate limits and derivatives, complete a complete function study, and solve applied mathematics problems.

There are no midterm exams. During the written exam, students can consult an A4 sheet of paper containing theory notes. The exam grade is calculated by adding the points assigned to the individual exercises; some problems consist of multiple questions, the scores of which are proportional to their intrinsic difficulty. A passing score of 18 is required. Some assignments from previous years will be published on the course's Moodle platform.

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, high mathematical rigor and excellent expository skills.

Front lectures;
Exercise sessions in class;
Lectures and classroom exercises aim to develop theoretical knowledge and practical skills in solving applied mathematical problems.
Learning materials are available on Moodle to support individual study and independent learning.