Learning objectives
Knowledge and understanding: At the end of this course, the student should know the essential definitions and results, and tools of Calculus 2 (differential calculus and integral calculus for real functions of several real variables, critical points and extremals, Taylor series expansion, Fourier series, Fourier transform), and he should be able to grasp how these enter in the solution of problems.
Applying knowledge and understanding: The student should be able to apply the aforementioned notions to solve mathematical problems not identical but strictly related to those already encountered, as well as to extrapolate the main results to be analyzed from a collection of data.
Making judgements: The student should be able to evaluate coherence and correctness of the solutions given during the written test, by constructing and developing logical arguments with a clear distinction of assumptions and conclusions; the student should be able to check correct proofs and spot wrong reasonings.
Communication skills: The student should be able to communicate in a clear and precise way, via a correct mathematical language, also through group work.
Prerequisites
Matematica I and Matematica II
Course unit content
The course of Mathematics III is designed to provide tools and mathematical methods (of the classical Calculus 2 program) useful for several applications in different scientific branches, as in particular in Chemistry; that is,
Differential calculus and integral calculus for real functions of several real variables, related critical points and extremals, Taylor series expansion, Fourier series, Fourier transform.
Full programme
- Functions of several real variables: limits; continuity and differentiability; maxima and minima.
- Curves and surfaces: integrals, Divergence Theorem; Stokes' Theorem;
- Series; functions series; Fourier series
- Fourier and Laplace transforms
Bibliography
M. Bramanti, C. D. Pagani, S. Salsa: Matematica (Calcolo Infinitesimale e Algebra lineare), Zanichelli Ed., in particular from Chapter 10 to Chapter 14
or, equivalently,
M. Bramanti, C. D. Pagani, S. Salsa: Analisi Matematica 2, Zanichelli Ed., in particular from Chapter 3 to Chapter 7
Also,
N. Fusco, P. Marcellini, C. Sbordone, Lezioni di Analisi Matematica Due, Zanichelli.
Teaching methods
The teaching consists in frontal lessons where both theoretical and applicable aspects are expounded. The exercises are selected so that the student will be able to solve independently many related problems arising from the theoretical lessons. During the course, the weekly student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis.
Further teaching support documents will be shared via the related Elly blog.
Assessment methods and criteria
Final written test(2h), and (possibly) in an oral discussion.
Other information
