CALCULATION WITH EXERCISES MOD. I
Basic knowledge of high school algebra, trigonometry and analytic geometry.
The course aims at introducing students to the fundamental methods and techniques of Mathematics, and in particular to the differential and integral calculus of one real variable and to sequences and series. A further goal is to train students in applying analytic techniques to other sciences.
Students will know the fundamental of differential and integral calculus of real functions of one real variable. In particular they will be able to study the qualitative graph of elementary function, to solve elementary ordinary differential equations, to determine the convergence of sequences and series; they will be able to state and prove the basics theorems of Analysis.
Number sets. Real and complex numbers. Topology of the real line. Limits of sequences and series.. Limits of functions and continuity. Continuous functions and topology. Differentiable functions and their properties. Differentiation rules. Fundamental theorems of the differential calculus. Taylor formula and second order conditions to determine the nature of a stationary point. Convexity. Study of the graph of a function. Riemann integral: definition of integrable function and properties of the integral. Classes of integrable functions. The fundamental theorem of calculus. Integration methods and computation of definite integrals. Improper integrals.
Analisi Matematica 1 lecture notes available at the page:
http://www.matapp.unimib.it/~demichele/libro.pdf
E. Giusti, Analisi Matematica 1, Boringhieri
E. Giusti, Complementi di Analisi Matematica 1, Boringhieri
M. Bramanti, C. Pagani, S, Salsa, Analisi Matematica 1, Zanichelli
Parent course
Borrowed from
click on the activity card to see more information, such as the teacher and descriptive texts.