The aim of the course is to give further knowledge and tools of calculus, required for an adequate understanding of mathematical methods and models relevant for engineering, including probability and statistics.
teacher profile teaching materials
Norm and distance in R^n. Functions of several variables. Continuous functions and Weierstrass theorem.
Partial derivatives, directional derivatives and gradient. Functions of class C^1 and C^2. Higher derivatives, Hessian matrix and Schwarz theorem. Differentiation of composed functions. Taylor expansion. Local maxima and minima. Method of Lagrange multipliers to compute local maxima and minima.
Riemann integration and Peano-Jordan measure. Integration of continuous functions, reduction formulae
and iterated integrals; area and volume. Change of variables in integrals and Jacobian matrix: polar, cylindrical and spherical coordinates. Gaussian integral.
Curves in R^n: parametrized and equivalent curves; length of a curve; curve integrals of scalar functions. Work and curve integrals of vector fields. Smooth surfaces in R^3: area of a surface and integrals on surfaces.
& Gentile, Introduzione ai Sistemi Dinamici Volume 1, Springer.
Esercizi: Marcellini, Sbordone, Esercitazioni di Analisi Matematica Due (vol. I e vol. II), Zanichelli ed.
Fruizione: 20801967 ANALISI MATEMATICA PER LE APPLICAZIONI in Ingegneria meccanica L-9 R N0 GENTILE GUIDO
Programme
Linear first-order differential equations. General first order differential equations. Cauchy problem: local existence and uniqueness. Separation of variables. Systems of first-order equations: linearly independent solutions and Wronskian matrix. Variation of constants. Differential equations with constant coefficients and characteristic polynomial. Matrix exponential and computation for diagonalizable matrices. Some remarkable differential equations: Euler equation and Bernouilli equation.Norm and distance in R^n. Functions of several variables. Continuous functions and Weierstrass theorem.
Partial derivatives, directional derivatives and gradient. Functions of class C^1 and C^2. Higher derivatives, Hessian matrix and Schwarz theorem. Differentiation of composed functions. Taylor expansion. Local maxima and minima. Method of Lagrange multipliers to compute local maxima and minima.
Riemann integration and Peano-Jordan measure. Integration of continuous functions, reduction formulae
and iterated integrals; area and volume. Change of variables in integrals and Jacobian matrix: polar, cylindrical and spherical coordinates. Gaussian integral.
Curves in R^n: parametrized and equivalent curves; length of a curve; curve integrals of scalar functions. Work and curve integrals of vector fields. Smooth surfaces in R^3: area of a surface and integrals on surfaces.
Core Documentation
Teoria ed esercizi: Bertsch, Dal Passo, Giacomelli, Analisi Matematica , McGraw Hill, II edizione,& Gentile, Introduzione ai Sistemi Dinamici Volume 1, Springer.
Esercizi: Marcellini, Sbordone, Esercitazioni di Analisi Matematica Due (vol. I e vol. II), Zanichelli ed.
Attendance
Attendance is not compulsory but is strongly recommended.Type of evaluation
The exam consists of a written test and an oral interview, to be carried out subsequently after the correction of the written test. The written test includes some exercises, in addition to a preliminary exercise, divided into 4 questions: only if at least 3 out of 4 answers are correct will the rest of the test be evaluated. Passing the written test (with a grade ≥18) allows you to take the oral interview in any session of the same academic year.