Mechanical Engineering

PART I 1 Sequences of functions 1.1 Poitwise convergence 1.2 Uniform convergence 1.3 Examples 1.4 Some theorems about the uniform convergence 1.5 Sufficient conditions 2 Series of functions 2.1 convergences 2.2 Uniform convergence results 3 Power series 3.1 Convergence radius 3.2 How to determine the radius 4 Taylor's series 4.1 Uniqueness of the expansion 4.2 Elementary functions expansion 5 Fourier series 5.1 Periodic functions and trigonometric polinomials 5.2 trigonometric series and Fourie series 5.3 Fourier Coefficients 5.4 Classes of functions 5.5 Fourier series convergence II PARTE 6 Complex numbers 6.1 Algebraic representation 6.2 Sum, difference 6.3 Polar coordinates and exponential notation 6.4 Product, quotient, power, root 6.5 Metric structure 6.6 Topological structure 7 Complex functions 7.1 limits 7.2 continuity 7.3 Examples 7.4 Discontinuos functions 8 holomorphic functions 8.1 Complex derivative 8.2 holomorphic functions 8.3 Cauchy-Riemann Conditions 8.4 complex exponential functions 8.5 complex trigonometric functions 8.6 complex hyperbolic functions 8.7 complex logarithm 8.8 complex power function 8.9 general complex exponential function 9 Complex power series 9.1 holomorphic functions and power series 10 complex integral 10.1 Curves 10.2 Change of coordinates 10.3 composition of curves 10.4 Line Integral 10.5 Primitive 10.6 Existence 10.7 simply connected open sets 10.8 differential forms and Gauss-Green Theorem 10.9 holomorphic functions and existence of a primitive 10.10 closed curve deformation priinciple 10.11 Firsti integral Cauchy formula 10.12 Derivative of holomorphic functions and second integral Cauchy formula 10.13 Harmonic functions 10.14 Morera Theorem 10.15 Cauchy inequality. Liouville Theorem. Algebra fundamental Theorem 11 Analitic functions 11.1Analitic functions and holomorphic functions 11.2 Zeros 11.3 Isolated zeros principle 11.4 Uniquenes of the analytic extension 12 Singularities 12.1 Isolaed singularities 12.2 Classification of singularities 13 bilateral and Laurent series 13.1 bilateral series 13.2 laurent serie in an annulus 13.3 Examples 13.4 Singularity and Laurent expansions 14 Residue 14.1 Defininition 14.2 Computatio in poles 14.3 Integral computation with the residue 14.4 Residue Theorem 15 Laplace transform 15.1 Definition 15.2 Properties 15.3 Derivative 15.4 Signals 15.5 periodic signals transform 15.6 derivative trasform 15.7 Inverse transform

One and multiple variables real functions, limits, continuity, derivability. Differential forms, curves in the plane, line integrals fo diufferential forms.

De Cicco-Giachetti Metodi Matematici per l’Ingegneria Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Either classical or electronic blackboard lectures.

Recommended

The exam consists in a written part (exercises and open questions to be solved in 2 hours), and in a short oral discussion, when the written part is passed with evaluation mark not below 18. The oral part takes place after the publication of the results of the written part, the exact day will be communicated contextually. Students who passed the written part and do not show-up to the oral part will be considered renunciative to the whole exam.

Carlo Presilla Elementi di Analisi Complessa Francis J. Flanigan Complex Variables Fusco-Marcellini-Sbordone Analisi Matematica Due

Either classical or electronic blackboard lectures.

PART I 1 Sequences of functions 1.1 Poitwise convergence 1.2 Uniform convergence 1.3 Examples 1.4 Some theorems about the uniform convergence 1.5 Sufficient conditions 2 Series of functions 2.1 convergences 2.2 Uniform convergence results 3 Power series 3.1 Convergence radius 3.2 How to determine the radius 4 Taylor's series 4.1 Uniqueness of the expansion 4.2 Elementary functions expansion 5 Fourier series 5.1 Periodic functions and trigonometric polinomials 5.2 trigonometric series and Fourie series 5.3 Fourier Coefficients 5.4 Classes of functions 5.5 Fourier series convergence II PARTE 6 Complex numbers 6.1 Algebraic representation 6.2 Sum, difference 6.3 Polar coordinates and exponential notation 6.4 Product, quotient, power, root 6.5 Metric structure 6.6 Topological structure 7 Complex functions 7.1 limits 7.2 continuity 7.3 Examples 7.4 Discontinuos functions 8 holomorphic functions 8.1 Complex derivative 8.2 holomorphic functions 8.3 Cauchy-Riemann Conditions 8.4 complex exponential functions 8.5 complex trigonometric functions 8.6 complex hyperbolic functions 8.7 complex logarithm 8.8 complex power function 8.9 general complex exponential function 9 Complex power series 9.1 holomorphic functions and power series 10 complex integral 10.1 Curves 10.2 Change of coordinates 10.3 composition of curves 10.4 Line Integral 10.5 Primitive 10.6 Existence 10.7 simply connected open sets 10.8 differential forms and Gauss-Green Theorem 10.9 holomorphic functions and existence of a primitive 10.10 closed curve deformation priinciple 10.11 Firsti integral Cauchy formula 10.12 Derivative of holomorphic functions and second integral Cauchy formula 10.13 Harmonic functions 10.14 Morera Theorem 10.15 Cauchy inequality. Liouville Theorem. Algebra fundamental Theorem 11 Analitic functions 11.1Analitic functions and holomorphic functions 11.2 Zeros 11.3 Isolated zeros principle 11.4 Uniquenes of the analytic extension 12 Singularities 12.1 Isolaed singularities 12.2 Classification of singularities 13 bilateral and Laurent series 13.1 bilateral series 13.2 laurent serie in an annulus 13.3 Examples 13.4 Singularity and Laurent expansions 14 Residue 14.1 Defininition 14.2 Computatio in poles 14.3 Integral computation with the residue 14.4 Residue Theorem 15 Laplace transform 15.1 Definition 15.2 Properties 15.3 Derivative 15.4 Signals 15.5 periodic signals transform 15.6 derivative trasform 15.7 Inverse transform

One and multiple variables real functions, limits, continuity, derivability. Differential forms, curves in the plane, line integrals fo diufferential forms.

De Cicco-Giachetti Metodi Matematici per l’Ingegneria Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Either classical or electronic blackboard lectures.

Recommended

The exam consists in a written part (exercises and open questions to be solved in 2 hours), and in a short oral discussion, when the written part is passed with evaluation mark not below 18. The oral part takes place after the publication of the results of the written part, the exact day will be communicated contextually. Students who passed the written part and do not show-up to the oral part will be considered renunciative to the whole exam.

Carlo Presilla Elementi di Analisi Complessa Francis J. Flanigan Complex Variables Fusco-Marcellini-Sbordone Analisi Matematica Due

Either classical or electronic blackboard lectures.

PART I 1 Functions sequences 2 Functions series 3 Power series 4 Taylor series 5 Fourier series PART II 6 Complex numbers 7 Functions of complex variable 8 Holomorphic functions 9 Power series in the complex numbers 10 Integration in complex variable 11 Complex analytic function 12 Singolarities 13 Residues 14 Bilateral series and Laurent series 15 Residues Theorem and applications 16 Laplace transform 17 Applications to differential equations

Mathematical Analysis I

Testi De Cicco - Giachetti: Metodi matematici per l’Ingegneria, Ed. Esculapio (Bologna) 2013 Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Non obbligatoria, in sede

Prova scritta

Testi De Cicco - Giachetti: Metodi matematici per l’Ingegneria, Ed. Esculapio (Bologna) 2013 Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Svolgimento tradizionale

PART I 1 Functions sequences 2 Functions series 3 Power series 4 Taylor series 5 Fourier series PART II 6 Complex numbers 7 Functions of complex variable 8 Holomorphic functions 9 Power series in the complex numbers 10 Integration in complex variable 11 Complex analytic function 12 Singolarities 13 Residues 14 Bilateral series and Laurent series 15 Residues Theorem and applications 16 Laplace transform 17 Applications to differential equations

Mathematical Analysis I

Testi De Cicco - Giachetti: Metodi matematici per l’Ingegneria, Ed. Esculapio (Bologna) 2013 Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Non obbligatoria, in sede

Prova scritta

Testi De Cicco - Giachetti: Metodi matematici per l’Ingegneria, Ed. Esculapio (Bologna) 2013 Casalvieri – De Cicco: Esercizi di Analisi matematica II, Ed. LaDotta (Bologna) 2017

Svolgimento tradizionale