


Politecnico di Torino  
Academic Year 2007/08  
03BJWEO Introduction to mathematics II 

1st degree and Bachelorlevel of the Bologna process in Architecture Sciences  Torino 





Objectives of the course
The goal of the unit is to widen the foundations of mathematics acquired throughout the unit "Introduction to mathematics I", both from a technicalinstrumental and educationalcultural point of view.

Expected skills
Upon completion of the units "Foundations of mathematics I" and "Foundations of mathematics II", the student will be able to use calculus, linear algebra and differential equation tools to solve a number of problems typical of applied sciences, and will be able to develop simple models relevant to his future area of research. The student will have learnt a method to deal with problems of different nature, in addition to the language used by modern culture to communicate a vast amount of information and thoughts.

Prerequisites
The knowledge acquired throughout the unit "Foundations of mathematics I" are sufficient to comprehend the contents of this unit.

Syllabus
Calculus: volumes of solids of revolution. Functions of two variables.
Linear algebra: vector spaces. Vector addition. Scalar product and vector product. Mixed product. Algebraic and geometric properties. Lines and planes in space. Matrices: elementary operations. Matrix determinant and rank. Systems of algebraic equations and their solutions. Eigenvalues and eigenvectors. Differential equations: solution by separation of variables. Linear equations (elastic line of a beam. Malthus Equation). Further methods of solution and Cauchy problem. Second order differential equations with constant coefficients. Kinematics of a material point (falling bodies, harmonic oscillator). 
Bibliography
R. Monaco e A. Repaci: Algebra lineare [Linear algebra], CELID;
R. Monaco: Le Equazioni Differenziali e le loro Applicazioni [Differential equations and applications], CELID; S. Lipschutz, Algebra Lineare [Linear algebra], Collana Schaum, Etas Libri; F. Ayres, Equazioni Differenziali [Differential equations], Collana Schaum, Etas Libri; R. A. Adams, Calcolo Differenziale [Differential calculus], Editrice Ambrosiana; P. Marcellini e C. Sbordone, Esercitazioni di Matematica [Math exercises], Liguori Editore. 
