


Politecnico di Torino  
Academic Year 2007/08  
20ACFHL, 20ACFHI Mathematical analysis I 

1st degree and Bachelorlevel of the Bologna process in Computer Engineering  Verres/Ivrea 1st degree and Bachelorlevel of the Bologna process in Mechatronic Engineering  Verres/Ivrea 





Objectives of the course
Objectives of the course
The aim of the course is to provide the student with the foundations of differential and integral calculus, together with a thorough grasp of all the basic concepts. Prerequisites Elementary analytic geometry in the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic equations and inequalities. 
Syllabus
Elementary logic. Sets, relations, functions. Composition of functions, inverse functions. Limits and continuity. Computation of limits. Discontinuities. Sequences. Landau symbols. Basic results on limits and on global properties of continuous functions. Derivatives and associated properties. The theorems of Fermat, Rolle, Lagrange, de l'Hopital. Taylor expansions. The fundamental theorem of calculus. Definite integrals. Improper integrals. 
Laboratories and/or exercises
Laboratories and/or exercises
These are supervised sessions in which students solve problems, either at the board or individually, under the supervision of a teacher. Attendance is compulsory for all those who did not obtain a sufficient mark in the mathematics part of the admisssion test. 
Bibliography
Bibliography
C. Canuto, A. Tabacco, Analisi Matematica 1, Springer 2005, Second Edition (complements can be downloaded from the site http://calvino.polito.it/canutotabacco/analisi_1 ) F. Fagnani, G. Grillo, Dispense di Analisi Matematica 1 (can be downloaded from the site http://calvino.polito.it/~fagnani/AnMat1/Anmat1.html ) Further information and additional exercises can be downloaded from the site http://calvino.polito.it/~terzafac  
