IN/0188 - MATHEMATICAL ANALYSIS 2
Academic Year 2016/2017
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STELLA PIRO (Tit.)
- Teaching style
- Lingua Insegnamento
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/10 - Ord. 2016] ELETTRICA||5||50|
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/20 - Ord. 2016] ELETTRONICA||5||50|
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/30 - Ord. 2016] INFORMATICA||5||50|
Introducing students in solving mathematical problems to be applied to engineering problems. In particular the students will be able to apply
differential and integral calculus for functions of several variable.
Good knowledge of Calculus 1 subjects
Functions in RN . Sets in RN : accumulation, isolated, internal , external, boundary points; bounded, open, closed, compact, connected sets.Functions of several variables in RN , domain, image; definition and properties of limits. Limit theorems. Continuity. Partial derivatives. Higher derivatives. The total differential. Tangent plane. Taylor formula. The chain rule. Implicit functions.
-Maxima and minima.
Local maximum and minimum. Critical points of a smooth function. The second derivative test. Maximum principle for harmonic functions. Maxima and minima with constraints.
-Curves and surfaces.
Plane Curves: parametric equations, implicit form, smooth, piecewise, simple, closed, oriented curves.Length of arc in parametric, Cartesian, polar form. Curves in R3 .Surfaces in R3: parametric and Cartesian form, normal vector to a surface.
Double integral. Integration over normal regions. Normal regions in polar coordinates. Triple integral: Integration over normal regions, cylindrical coordinates and applications. Volume.
-Line and surface integrals. Line integrals, applications. Area of smooth surfaces, of a surface of revolution. Surfaces Integrals. Flux.
-Green’s theorem, Stokes’ theorem and their applications.
Frontal lectures (theory): 31 hours
Frontal lectures (exercises): 19 hours
Tutor activity is scheduled.
Verification of learning
Final exam: a test exam, consisting on solving several exercises and proving some theorems. An eventual discussion.
Marco Bramanti, Carlo D. Pagani, Sandro Salsa: Analisi matematica 2. Zanichelli,
Sandro Salsa, Annamaria Squellati: Esercizi di Analisi matematica 2, Zanichelli
Tests of previous exams are available during office hours or in the site
for the students.