The main goal of the course is give the basis of calculus of one variable functions, with the adjoint of the basis of linear algebra.
Particular attention will be devoted to the study of examples.
Knoledge e comprehension: the students will have to
learn the fundamental tools of mathematical analysis, with particular regard to the logical understanding of definitions and theorems and the identification of examples and counter-examples.
Ability to Apply Knowledge and Understanding: The students will have to acquire the knowledge in solving the main problems regarding linear algebra and the study of functions of one variable. This will involve the ability to identify appropriate theoretical tools
suitable to the particular problem under study by applying correctly the tools of linear algebra and
Autonomy of judgment: Students must be able to know how to establish the logical veracity of affirmations and properties regarding the functions of a variable.
Communication Skills: Students must be able to expose in a formally correct logical way the theorems concerning linear algebra arguments and the theory of the functions of one variable, highlighting hypothesis and thesis and illustrating the results through examples and applications.
Learning Skills: The student must be able to update and deepen the discussed topics, also by identifying the appropriate tools among those available on the web.
It is necessary the knowledge of trigonometry, and the resolution tools of algebraic equations, inequalities
and systems of algebraic equations and inequalities.
Linear Algebra: basis of vector spaces; linear dependence, matrices, determinant and rank. Cramer and Rouché-Capelli Theorem; Linear applications; kernel and image; eigenvalues and eigenvectors.
Cartesian plane, lines and planes in the space.
Complex numbers: algebraic and polar forms; powers and roots.
Functions of one variable: definition, injectivity, inverse function. Examples: absolute value, power,
exponential, trogonometric functions, sequences.
Limit: definitions, computation, limit of particular interest. Continuity: definition; principal theorems
concerning continuous functions.
Differential calculus: derivatives, tangent line, optimization; Taylor formula; convexity property.
Integral calulus: definition of the Cauchy-Riemann integral; integration by parts; integration of rational functions; changing variable in the integration; Calculus of areas. Torricelli-Barrow Theorem.
G. Crasta, A. Malusa: “Matematica 1".
M. Bramanti, C. Pagani, S. Salsa: “Matematica (calcolo infinitesimale e algebra lineare)” e Salsa-Squellati: “Esercizi di Matematica – Volume 1”.
Notes by the teacher.
Written and oral test.