Università degli Studi di Perugia

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Teaching: Mathematics

Degree CourseDegree course in Agricultural and Environmental Sciences [L-25] D. M. 270/2004
CurriculumAGRICOLTURA SOSTENIBILE - Regulations 2014
PrerequisitesInformation currently not available - Italian version
Assessment methods

Written and Oral exam.

It is possible to have some progress assessments and a final oral exam

Examinations' grades statisticsInformation currently not available - Italian version
Examinations' dates

Check online information at www.agr.unipg.it

Recommended optional coursesInformation currently not available - Italian version
LecturerLuca Zampogni
TypeBasic formative activities
Implementation proceduresConventional
Course content

A - B. Functions, Equations and inequalities (2CFU) . Definition of a single-valued function. Monotonic and inverse functions. Operation with functions, composite functions. Algebraic functions: linear, quadratic, cubic, rational, n-th root, absolute-value, integer part function. Trigonometric functions. Geometric transformations : translations and reflections. Using Excel or Computer Algebra Systems to explore the main properties in their graphs.
Linear, quadratic, rational, irrational, modulus (absolute value) equations and inequalities. Linear systems, Cramer's rule.

C. Iterative processes - Exponential functions (1 CFU). Sequences, recursive formulas. Arithmetic and geometric progressions.
Logarithmic and exponential functions and their graphs. Logarithmic and exponential equations and inequalities.
Iterative processes: mitosis, Fibonacci sequence, simple and compound interest in Economy, radioactive decay. Semilogarithmic coordinate systems.

D. Limits (1 CFU). Introduction to limits. Theorem on uniqueness of the limit. Infinite limits and limits at infinity. Continuity of a function: definition and basic theorems. The types of discontinuity. The calculation of limits. Some special limits. The squeezing Theorem.

E . Derivatives (1 CFU). Tangent lines and derivatives : geometric interpretation. The average rate of change, the derivative as the rate of change. Some differentiation formulas. The derivative of composite and inverse functions. The L'Hôpital's Theorem. Critical points and local extrema of functions. The Férmat's Theorem. Concavity, convexity, derivative test for convexity.

F. Integral (1CFU). Riemann integral. The method of exhaustion. The area of regions between two graphs. Mean value theorems for integrals. Indefinite integrals. Fundamental theorem of integral calculus. Integration by substitution (elementary integrals).


To provide students with basic knowledge about formulating, solving and discussing simple mathematical models in biology, economy, engineering. Elementary functions. Equations and inequalities. Sequences, iterative process. Limit, continuity, derivative. Riemann integral and the area of regions between two graphs.

Mode of delivery

Lectures: 42 hours.
Exercises: 18 hours.
Tutor teaching activities: 40 hours.
On line lectures notes.

Recommended reading

1. J. Stewart, "Calcolo. Funzioni di una variabile", APOGEO (2001).
2.  Lecture notes available online on the Moodle platform (please ask to the faculty secretariat for more information)

Learning outcomes

1. Elementary functions, exponential and logarithmic maps.
2. Sequences
3. Limits.
4. Continuity of functions.
5. Derivatives and applications. Some elements of differential calculus.
6. Critical and extremal points.
7. Integrals and applications.

1. To define and analyze simple mathematical models.
2. To solve equalities and inequalities of various kind.
3. To draw, interpret and study the graphs of functions.
4. To compute limits, derivatives and integrals.

Teaching period

To be announced (check the webpage www.agr.unipg.it)

Teaching calendar

To be announced (check the webpage www.agr.unipg.it)

Teaching support

Pre-course lessons: from September 17 to October 12, 2012

Tutor teaching activities: to be announced (more information will be available as soon as possible at the page www.agr.unipg.it and at the Moodle platform).

Teaching languageItalian

Not compulsory.


Facoltà di Agraria, Università degli Studi di Perugia, Borgo XX Giugno 74, Perugia.

Individual study
Integration to teaching activity
Luca Zampogni
PeriodI semester II semester 
NotesInformation currently not available - Italian version
Consulting hours

See the web page of the Department and the Moodle page of the course

Consulting location

DSA3, Department of Hydraulics Engineering

ECTS code2014 - 1217

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