


Politecnico di Torino  
Academic Year 2009/10  
02BQYDR, 02BQYAX, 02BQYAY, 02BQYDS Mathematical methods for engineering I 

1st degree and Bachelorlevel of the Bologna process in Mechanical Engineering  Vercelli 1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Vercelli Master of sciencelevel of the Bologna process in Civil Engineering  Vercelli Espandi... 





Objectives of the course
The goal of this course is to learn multivariate calculus which is fundamental for engineering applications.

Expected skills
The student will be able to deal with elementary analytic geometry in the space, study multivariate functions and to compute integrals both on curves or surfaces and on multivariate domains.

Prerequisites
The students are expected to know results and techniques from calculus in one variable, linear algebra (matrix, vector spaces, eigenvalues and quadratic forms, trigonometry and plane geometry.

Syllabus
 Elements of space geometry: lines, planes , plane space curves, conics, surfaces, quadrics, cones and
 cylinders.  Parametric space curves, tangent line and length of a curve. Integration along a curve.  Topology of real ndimensional spaces; continuity of multivariate functions, gradients and directional derivatives. Maxima and Minima, constrained Extrema and Lagrange multipliers.  Parametric surfaces, rotational surfaces, graphs of two variable functions, plane and spatial regular transformations.  Vector fields, rotational fields. Integrals on curves, exact differentials.  Multiple integration: double and triple integrals. Integrals in polar, cylindrical and spherical coordinates. GaussGreen formula and Stoke's Theorem. 
Laboratories and/or exercises
Exercise sections are done during the course.

Bibliography
S.Greco, P.Valabrega, Lezioni di Geometria, ed.Levrotto e Bella.
A.Sanini, Elementi di Geometria, ed.Levrotto e Bella. M.Bramanti, C.D.Pagani, S.Salsa, MATEMATICA, calcolo infinitesimale e algebra lineare, ed. Zanichelli. S.Salsa, A.Squellati, ESERCIZI DI MATEMATICA, calcolo infinitesimale e algebra lineare Vol.2, , ed. Zanichelli. Fusco N., Marcellini P., Sbordone C., Elementi di Analisi Matematica II, ed. Liguori. 
Revisions / Exam
The examination consists in a written proof based on resolution of exercises.
No calculator, no texts or notes can be used during the examination. 
