MATHEMATICAL ANALYSIS 1
OVERVIEW
The aim of this course is to provide a practical working tool for students in Engineering or in any other field where rigorous
Calculus is needed. The basic focus is on functions of one real variable and basic ordinary differential equations, separation
of variables, linear first-order, and constant coefficients ODE.
AIMS AND CONTENT
LEARNING OUTCOMES
The aim is to achieve good knowledge of differential and integral calculus for one or two variables functions.
AIMS AND LEARNING OUTCOMES
The student will have to acquire a solid ability in Mathematical Analysis, in particular he must know how to study a function of one or more real variables. Moreover he will have to know how to apply the various theorems for the resolution of simple differential equations of the first order and higher order (linear with constant coefficients).
PREREQUISITES
Elementary algebra: equations and inequalities, trigonometry.
Teaching methods
106 hours of lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course many exercises will be solved. During the academic year some guided exercises will be carried out.
SYLLABUS/CONTENT
Real numbers, infimum and supremum, functions of one real variable, elementary functions, limits, infinitesimals and infinities, continuous functions, derivable functions, differentiable functions, Taylor’s formula, expansion of elementary functions, primitives and indefinite integrals, methods of indefinite integration, definite integrals, fundamental theorem of integral calculus, first order differential equations, Cauchy’s problem and theorem, resolution of linear first order differential equations and separable variables equations, linear differential equations with constant coefficients of order n.
RECOMMENDED READING/BIBLIOGRAPHY
F. Parodi, T. Zolezzi, Appunti di Analisi matematica, ECIG, 2007
R. A. Adams, Calcolo differenziale 1 & 2, Casa Editrice Ambrosiana, 2007
A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991.
M. Bramanti, C. Pagani, S. Salsa, Analisi matematica 1 e 2 Zannichelli, 2008
M.Baronti-F.De Mari-R.Van Der Putten-I.Venturi: Calculus Problems, Springer
TEACHERS AND EXAM BOARD
Ricevimento: The teacher is available for explanations one afternoon a week.
Exam Board
MARCO BARONTI (President)
CLAUDIO ESTATICO
ROBERTUS VAN DER PUTTEN (President Substitute)
LESSONS
Teaching methods
106 hours of lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course many exercises will be solved. During the academic year some guided exercises will be carried out.
LESSONS START
Lessons start on September.
EXAMS
Exam description
The final exam consists of a written test and an oral exam. The student must obtain an evaluation of at least 12/30 in the written test to access the oral exam.
Assessment methods
During the written test the student will have to solve some exercises concerning the study of functions and the differential problem. During the oral examination the student must highlight critical analytical skills and must be able to apply the main theorems for the solution of easy exercises.
Exam schedule
Date | Time | Location | Type | Notes |
---|---|---|---|---|
08/06/2021 | 09:30 | LA SPEZIA | Scritto | |
12/07/2021 | 09:30 | LA SPEZIA | Scritto | |
14/09/2021 | 09:30 | LA SPEZIA | Scritto |