Università degli studi dell'Insubria

# Mathematics

Degree course:
Corso di First cycle degree in ENVIRONMENTAL AND NATURAL SCIENCES
Academyc year when starting the degree:
2018/2019
Year:
1
Academyc year when helding the course:
2018/2019
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

Written and oral examination

Assessment:
Voto Finale

TEACHING OBJECTIVES AND EXPECTED LEARNING RESULTS
• Acquisition of theoretical and operational skills in the field of differential and integral calculus
• Acquisition of the rudiments of Probability Calculus and Statistics
• Acquisition of Algebra basics
• Acquisition of the basic notions of Numerical Calculus

LEARNING PROCEDURE METHODS
The exam consists of a written and oral test. The written test provides simple exercises also in the form of a quiz. The oral exam consists in the discussion of the written and in the exposition of the concepts studied in the course. The written part is not graded, but serves as a starting point for the overall vote.

Real numbers - elementary properties of real numbers. Absolute value. Power and logarithm. Lower and upper extremity

Functions and Limits - monotone functions. Limits and their properties. Continuity and fundamental properties of continuous functions.

Basic functions - Trigonometric, exponential, hyperbolic and inverse functions.

Differential calculus - Derivatives of real functions and their properties. Theorems of Rolle, Lagrange and Cauchy. Computation of limits with the De l'Hopital method. Taylor polynomials.

Integral calculus - Definite integrals. Integration of continuous functions. Integral functions. First and second fundamental Theorem of Calculus. Indefinited integrals. Integration by parts and by substitution.

Differential equations - Overview of the first order differential equations. Solution of the Cauchy problem for linear equations and separable variables.

Algebra - Real vector spaces. Matrices and linear applications. Determinants. Solutions of linear systems of equations.

Complex Numbers - The complex field as an extension of the real one. The Complex plane. Vector, polar, exponential form. Geometry of the sum and product operations in the complex plane. N-th roots of a complex number.

Statistics - Media, mode, median. Standard deviation and variance. Least squares - Statistical significance.
Graphic representations and how to interpret them.

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Classroom lessons

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