Lecturer: Elena Bonetti  

Course name: Calculus (Mathematical analysis)
Course code: 500446
Degree course: Ingegneria Meccatronica, Ingegneria per l'Ambiente e il Territorio
Disciplinary field of science: MAT/05
University credits: CFU 12
Course website: http://www-dimat.unipv.it/bonetti

Specific course objectives

The course deals with the notions of calculus required for a faculty of engineering: differential and integral calculus for scalar and vectorial real functions, the infinitesimal calculus for curves and surfaces, the differential equations. The student is assumed to tackle problems as optimization, applications in geometry and mechanics, modeling simple situations by use of differential systems, using Stokes and Gauss theorems to describe balance laws.

Course programme

Differential calculus

Real and complex fields
• real and vectorial functions and graphs
• sequences
• series
• limits
• continuous functions
• differentiability
• derivability
• polinomial approximations
• series of functions
• optimization
• curves and surfaces

Integral calculus

Cauchy-Riemann integrals
• Integration techniques
• Integral functions
• The fundamental theorem of integral calculus
• Improper integrals
• Integrals on curves (I and II type)
• Integrals on surfaces
• Vector functions, potentials, works
• Gauss and Stokes theorems
• Applications to physics laws (from balance laws to differential equations)

Differential equations

Difefrential models
• Cauchy problems
• First order linear equations
• Second order linear equations with constant coefficients

Course entry requirements

Required by the faculty for beginners

Course structure and teaching

Lectures (hours/year in lecture theatre): 60
Practical class (hours/year in lecture theatre): 60
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

Bramanti, Pagani, Salsa. Matematica, Calcolo infinitesimale e algebra lineare. Ed. Zanichelli.

Testing and exams

Examination: solving exercises and interrogation