First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INM0016658, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course 5 years single cycle degree in
IN0533, Degree course structure A.Y. 2010/11, A.Y. 2018/19
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination CALCULUS 1
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit CANNOT be attended under the option Single Course unit attendance
Optional Course unit The Course unit is available ONLY for students enrolled in BUILDING ENGINEERING AND ARCHITECTURE

Teacher in charge LUCA BERGAMASCHI MAT/08

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 6.0 63 87.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019

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 real-valued 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 real-valued 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. Real-valued sequences, limits. Theorems on limits for sequences.
Real-valued 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 real-valued 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. Cerca nel catalogo
  • Barozzi Gonzalez, Esercizi di Analisi Matematica. Padova: Progetto, 2010. Cerca nel catalogo