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Facoltā di Scienze Agrarie e Alimentari Universitā degli Studi di Milano
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Calculus
Code: G300G-
Teacher:  Silvia Maria Carla Annaratone
Year: 
Term: 
CFU: 
CFU subdivision: Lectures: 5
Practices in classroom: 3
Basic aims:  The course intends to treat some mathematical concepts
and methods, particularly usefull for the application to
Agricultural Sciences. The aim of the course is help the
student to gain an adeuqate theoretical understanding of
the matter, as well as adequate computational skill.
Acquired skills:  Knowledge and understanding of basic concepts of
calculus in one variable, solution of exercises related to
the topics developed during the courses
Course contents:  Numerical sets. The coordinate plane: straight lines,
parabolas, circles. Elementary functions. Equations,
inequalities and system of algebraic and irrational
inequalities. Generalities about real funcion. Limits.
Continuity. Asymptotes. Differential calculus.
Monotonicity. Global maxima and minima. Convexity and
concavity. Integral calculus.
Program:  Numerical sets.: N, Z, Q e R. The coordinate plane:
straight lines, parabolas, circles. Elementary functions
and their graph. Equations, inequalities and system of
algebraic and irrational inequalities. Generalities about
real funcion: domain, range, injective and surjective
functions, composed functions, inverse functions,
geometric transforms of elementary functions. Limits:
computing limits, comparison of infinites and
infinitesimals, indeterminate forms. Continuity.
Asymptotes: vertical, horizontal and slant. Differential
calculus: first derivative, tangent line, monotonicity,
global and local maxima and minima. Second derivative:
convexity and concavity, inflection points. Integral
calculus. Computation of plane areas.
Prerequisites:  Integers, rational and real numbers. Literal Calculus.
Equations and inequalities. Eponential and logarithm.
Outline of Analytic geometry (Coordinates and lines)
Preparatory instructions:  none
Learning materials:  agrimat and matematica assistita: free download at
http://ariel.ctu.unimi.it/corsi/mateassistita
Other info:  The final mark is the outcome of a written and an oral
exam that are both compulsory. The written exam
(whose mark is at most 30/30) is made of two part, A
and B that take place the same day. Part A takes half
an hour and it focuses on the prerequisities. It consists
in 10 problems to be solved quickly. Only if the student
answers correctly at least 8 questions, his part B will
be evaluated. Part B takes two hours and consists of a
few open-ended question regarding the exam program.
The oral examination consists of a short conversation
about the topics of the program, which aims to
establish definitively what tools the student has
acquired in the study of mathematics.
DOWNLOAD
Program of Calculus (pdf version)
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