
Course unit
INSTITUTIONS OF MATHEMATICS
SCN1028295, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Practice 
2.0 
32 
18.0 
No turn 
Lecture 
5.0 
40 
85.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
8 ISTITUZIONI DI MATEMATICA 20192020 
01/10/2019 
27/11/2020 
ZANARDO
PAOLO
(Presidente)
LUCCHINI
ANDREA
(Membro Effettivo)
DI SUMMA
MARCO
(Supplente)

7 ISTITUZIONI DI MATEMATICA 20182019 
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 highschool.
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 threedimensional 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 pointplane and pointline. 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, .

Giuliano Artico, 333 ESERCIZI SVOLTI. Padova: Edizioni Libreria Progetto, .

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Questioning
 Problem solving
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

