First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCN1028295, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
SC1165, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination INSTITUTIONS OF MATHEMATICS
Website of the academic structure
Department of reference Department of Biology
E-Learning website
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge PAOLO ZANARDO MAT/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/02 Algebra 2.0
Basic courses MAT/03 Geometry 3.0
Basic courses MAT/05 Mathematical Analysis 2.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 32 18.0 No turn
Lecture 5.0 40 85.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
8 ISTITUZIONI DI MATEMATICA 2019-2020 01/10/2019 27/11/2020 ZANARDO PAOLO (Presidente)
LUCCHINI ANDREA (Membro Effettivo)
DI SUMMA MARCO (Supplente)
7 ISTITUZIONI DI MATEMATICA 2018-2019 01/10/2018 30/11/2019 ZANARDO PAOLO (Presidente)
LUCCHINI ANDREA (Membro Effettivo)
DI SUMMA MARCO (Supplente)

Prerequisites: To follow the Course, the student is supposed to thoroughly know the following topics, that are taught in the high-school.
Equations and inequalities of degree one and two; fractional inequalities.
Equation of line, parabola and circle in the Cartesian plane.
Trigonometry: main relations.
Properties of powers and logarithms.
Target skills and knowledge: The Course gives the basic notions of differential and integral calculus for functions of a real variable and the fundamental facts on geometric vectors, lines and planes on the three-dimensional space, differential equations. The student will be able to solve problems and exercises, applying the notions studied, like problems on related velocities, applications of the derivative, applications of differential equations.
Examination methods: Written exam, consisting of five exercises:
1) Study of a function, 11 points;
2) Either related velocities or MAX/MIN probems, 5 points;
3) Computation of areas using integrals, 5 points;
4) Analytic Geometry, 6 points;
5) Solving of a differential equation, 6 points.
The exercises and problems are standard and similar to those made in the classroom.
Assessment criteria: The total grade is based on the grades of the exercises in the written test. The grade of each exercise and the criteria of evaluation are explained to the students in detail.
Course unit contents: Functions of a real variable. Graphs of elementary functions: modulus, exponential, logarithm, sinus, cosinus, tangent. Inverse function. arcsin, arccos, arctg and their graphs.

Definition of limit. Graph representation of limits; property of limits. Operations with limits. Undetermined forms. Sequences of real numbers and their limits (outline).

Continuous functions. Graph representations of Weierstrass, zeros and values theorems. Substitutions in limits. Fundamental limits. The number e and the natural logarithm.

Derivative: its meaning in geometry and physics. Derivatives of elementary functions. Operations with derivatives. Theorems and Rolle and Lagrange; consequences. L'Hopital Rule. Derivatives of larger order. Relative max and min. Convexity, flexes. Asimptotes. Study of a function, draw of its graph.

Applications of derivatives. Related velocities. Max/min problems.

The concept of differential. Primitives of a function. Indefinite integral. Integration by substitution, for parts. Integration of rational functions; undetermined coefficients.
Defined integral. The theorem of integral media and the fundamental theorem of calculus. Computation of areas by integration. Volume of solid of rotation. Generalized integrals.

Vectors. Sums and multiples of vectors, scalar product. Determinant of a matrix. Vector product. Mixed product. Equation of a plane in the space. Various kinds of equations of a line. Sheaf of planes. Distance point-plane and point-line. Distance of two lines.

General notions on Differential Equations. First order differential equations. Various applications. Growth of a population. Separable differential equations.

Many exercises are made on each topic of the Course, for two credits of "Esercitazioni".
Planned learning activities and teaching methods: Frontal lessons made by the professor, using the blackboard. During the lesson, comments and questions by the students are welcome.
Additional notes about suggested reading: The suggested books are useful to get a deeper knowledge of the matter taught in the classroom. One may found online many tests of exam from the past years.
Textbooks (and optional supplementary readings)
  • Giuliano Artico, ISTITUZIONI DI MATEMATICA - Primo corso di matematica per la laurea triennale. Padova: Edizioni Libreria Progetto, --. Cerca nel catalogo
  • Giuliano Artico, 333 ESERCIZI SVOLTI. Padova: Edizioni Libreria Progetto, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Questioning
  • Problem solving

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)

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