
Course unit
CALCULUS 1
INM0016658, 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/05 
Mathematical Analysis 
6.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
63 
87.0 
No turn 
Prerequisites:

Solution of inequalities and systems. Properties of geomatrical loci such as parabolas and circles. 
Target skills and knowledge:

Ability to acquire mathematical reasoning. Learning how to prove a theorem.
Acquiring technique to solve problems such: computation of extremals of a function, calculus of integrals, approximate function via polynomials, limits of realvalued functions 
Examination methods:

Written examination + optional oral exam 
Assessment criteria:

The written exam consists of exercises such as draw the graph of a function, limit of a realvalued functions/sequences, integrals
and also some theoretical questions (statements, proofs, etc.).
If the mark of the written exam is larger than 24/30, there is a mandatory oral examination to possibly confirm the grade. 
Course unit contents:

Natural numbers. Classification of set of numbers. Assiomatic definition of real numbers. Completeness of real numbers. Supremum/infimum. Realvalued sequences, limits. Theorems on limits for sequences.
Realvalued functions, continuity. Theorem of Bolzano. Limits of fucntions. Derivative of a function. Geometric intepretation. Rules of derivation. Convexity.
The fundamental theorem of integral calculus. Functions: logarithm, exponential, trigonometric functions. Integration rules.
Theorems of the differential calculus. The Taylor formula. Exercises on calculus of limits via Taylor formula. 
Planned learning activities and teaching methods:

The lessons will be given mainly in class. The teacher first introduces the students to the mathematical language. Most of the lectures will be devoted also to the technique of solving exercise such as: calculus of limits, derivatives, integrals, graph of functions, maxima and minima of realvalued functions. 
Additional notes about suggested reading:

There are two suggested textbooks which cover both theory and exercises. Also notes taken during the lessons are very useful to complete the information.
Moreover the teacher almost every week uploads on the Moodle page of the course some sets of exercises including those taken from past written exams. 
Textbooks (and optional supplementary readings) 

Luca Bergamaschi, Fondamenti di Analisi Matematica. Padova: Ed. Progetto, 2017.

Barozzi Gonzalez, Esercizi di Analisi Matematica. Padova: Progetto, 2010.


