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B015498 - MATHEMATICS II
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2013-14
Course year
First year - Second Semester
Belonging Department
Physics and Astronomy
Course Type
Single education field course
Scientific Area
MAT/02 - ALGEBRA
Credits
6
Teaching Hours
48
Teaching Term
03/03/2014 ⇒ 13/06/2014
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
italian
Course Content
Integrals of the functions in one real variable. Simple Ordinary Differential Equations. Integral Calculus for the functions in several real variables. Line and surface integrals. Vector fields. Gauss and Stokes Theorems
Suggested readings (Search our library's catalogue)
N. Fusco, P. Marcellini, C. Sbordone: “Elementi di analisi matematica II. Versione semplificata per i nuovi corsi di laurea”, Liguori Editore.
Enrico Giusti: “Analisi matematica II”.
M. Bertsch, R. Del Passo, L. Giacomelli: “Analisi matematica”, McGraw-Hill.
P. Marcellini, C. Sbordone: “Esercitazioni di matematica, Secondo Volume, Volume 2.1 e Volume 2.2”, Liguori Editore.
Enrico Giusti: “Analisi matematica II”.
M. Bertsch, R. Del Passo, L. Giacomelli: “Analisi matematica”, McGraw-Hill.
P. Marcellini, C. Sbordone: “Esercitazioni di matematica, Secondo Volume, Volume 2.1 e Volume 2.2”, Liguori Editore.
Learning Objectives
Knowledge acquired: Basic elements of Integral Calculus and of the linear and non-linear Ordinary Differential Equations Theory.
Competence acquired:
To know how to solve the most common definite, indefinite and improper integrals. To know how to solve the standard Ordinary Differential Equations.
Skills acquired (at the end of the course):
To be able to pick out and use the tools of integral calculus and of the ODE suited to solve problems in optometry.
Competence acquired:
To know how to solve the most common definite, indefinite and improper integrals. To know how to solve the standard Ordinary Differential Equations.
Skills acquired (at the end of the course):
To be able to pick out and use the tools of integral calculus and of the ODE suited to solve problems in optometry.
Prerequisites
Arguments of the course of Mathematics II
Teaching Methods
Frontal lessons and exercises
Type of Assessment
Written text and oral text
Course program
Definite integrals – Method of
Exhaustion. Definitions and
Notations. Properties
Of the definite integrals.
Theorem of the mean value for integration (only the statement).
Indefinite integrals.
Primitive integrals.
Fundamental theorem of calculus. Primitive integrals.
Integration for decomposition in sum. Integration of the rational functions.
Integration for parts.
Integration for substitution.
Calculation of areas
of plane figures.
Improper integrals.
Multiple integrals. Double integrals on normal sets.
Reduction formulas.
Change of variables in
double integrals. Cartesian
coordinates and
polar coordinates.
Numerical series. Non negative term series. The geometric series.
The harmonic series. The generalized harmonic series.
Convergence criteria.
Leibniz criterion for the alternating series.
Absolute convergence.
Power series. Radius of
Convergence. Mentions of the
Taylor series.
Differential equations of the first order, linear and nonlinear, homogeneus and non
homogeneus. Separable differential equations.
Bernoulli equations.
Method of
variation of the constants.
Mention of the Cauchy problem.
Exercises about all topics of the course.
Exhaustion. Definitions and
Notations. Properties
Of the definite integrals.
Theorem of the mean value for integration (only the statement).
Indefinite integrals.
Primitive integrals.
Fundamental theorem of calculus. Primitive integrals.
Integration for decomposition in sum. Integration of the rational functions.
Integration for parts.
Integration for substitution.
Calculation of areas
of plane figures.
Improper integrals.
Multiple integrals. Double integrals on normal sets.
Reduction formulas.
Change of variables in
double integrals. Cartesian
coordinates and
polar coordinates.
Numerical series. Non negative term series. The geometric series.
The harmonic series. The generalized harmonic series.
Convergence criteria.
Leibniz criterion for the alternating series.
Absolute convergence.
Power series. Radius of
Convergence. Mentions of the
Taylor series.
Differential equations of the first order, linear and nonlinear, homogeneus and non
homogeneus. Separable differential equations.
Bernoulli equations.
Method of
variation of the constants.
Mention of the Cauchy problem.
Exercises about all topics of the course.