# Mathematics

Degree course:
Corso di First cycle degree in ENVIRONMENTAL AND NATURAL SCIENCES
Academyc year when starting the degree:
2015/2016
Year:
1
Academyc year when helding the course:
2015/2016
Course type:
Basic compulsory subjects
Credits:
9
Period:
First Semester
Standard lectures hours:
72
Detail of lecture’s hours:
Lesson (72 hours)
Requirements:

The course does not require special prerequisites.

Final Examination:
Orale
Assessment:
Voto Finale

Objectives of the course and learning outcomes

Acquisition of theoretical and operational capabilities in the field of differential and integral calculus
Acquisition of rudiments of Probability
Acquisition of basic knowledge of Algebra

Assessment methods
The exam consists of a written and oral test. The written test includes simple exercises also in the form of quizzes. The oral exam consists of the discussion of the written test and the exposition of the concepts studied in the course

1- Real numbers - Elementary properties of real numbers. Absolute value. Power and logarithm. Sup and Inf.
2- Functions and Limits - Monotone functions. Limits and their property. Continuity and properties of continuous functions. Basic functions - Trigonometric functions, exponential, hyperbolic and their inverses.
3-Calculus - Derivatives of a real function and their properties. Theorems of Rolle, Lagrange and Cauchy. Computation of limits by the l’Hopital’s rule. Taylor polynomials.
4- Integral calculus - Definite integrals. Integration of continuous functions. Integral functions. First and Second Fundamental Theorem of Calculus. Indefinite integrals. Integration by parts and by substitution.
5- Differential equations - Introduction to differential equations of the first order. Solution of the Cauchy problem for linear equations and separation of variables. Algebra - Real vector spaces. Matrices and linear applications. Determinant. Solution of linear equations.
6- Complex Numbers – The complex field as an extension of the real one. The Complex plan. Vector representation, polar representation and exponential representation of a complex number. Geometric meaning of the operations of sum and product in the complex plane. N-th roots of a complex number.

Any university level text on the subject.