- Docente: Paolo Negrini
- Credits: 13
- SSD: MAT/03
- Language: Italian
- Moduli: Paolo Negrini (Modulo 1) Hans Joachim Rudiger Achilles (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Ravenna
- Corso: First cycle degree programme (L) in Chemistry and Technologies for the Environment and Materials (cod. 8515)
Course contents
Real numbers; inequalities; absolute value.
elementary real functions: power functions, roots, exponential and
logarithm; circular and hyperbolic functions and their
inverses.
limits and continuity; basic theorems.
derivatives. basic theorems and applications: tangents to curves,
increasing and decreasing functions, convexity; graphs of
functions; Taylor's formula.
Complex
numbers. Definition, operations, properties. Module and
argument. Trigonometric representation. De Moivre's formula. n-th
roots of complex numbers
integrals in one variable. primitives; integration of rational
functions, integration by substitution and by parts.
ordinary differential equations. methods to solve first order
o.d.e. of linear type or separate variables type, and linear o.d.e.
of higher order whith constant coefficients.
first elements of differential calculus for several variables.
partial derivatives; gradient and hessian matrix. maxima and
minima. Double integrals: geometric meaning, calculus by reduction;
change of variables; use of polar coordinates.
Second Course Module (Prof. Rüdiger Achilles -
http://www.dm.unibo.it/~achilles/)
This course module will hopefully cover the material of the
first
six chapters of the recommended book:
floating-point numbers, complex numbers, vectors and matrices,
functions,
nonlinear equations, approximation of functions and data (in
particular,
trigonometric interpolation and fast Fourier transform, the
least-squares
method), numerical differentiation and integration, linear
systems,
eigenvalues and eigenvectors.
To experience the introduced methods and algorithms, the MATLAB and
Octave
programming environments are used.
Readings/Bibliography
Paolo Negrini, EQUAZIONI DIFFERENZIALI, Pitagora, Bologna
1999
A. Quarteroni, F. Saleri, Scientific Computing with MATLAB and
Octave.
Second Edition, Springer Berlin Heidelberg New York, 2006.
Teaching methods
Lessons accompanied by exercise classes and laboratory activities
in
MATLAB/Octave programming. Support by a tutor is offered for
free.
Assessment methods
Written examination concerning problem solving followed by an oral
examination,
which includes the discussion of a programming project.
Teaching tools
Exercises for homework and course material are available at
http://www.dm.unibo.it/~achilles/calc/.
http://campus.unibo.it/cgi/lista?annoAccademico=2011&idComponenteAF=366492
Office hours
See the website of Paolo Negrini
See the website of Hans Joachim Rudiger Achilles