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Generalizations to triple integrals. Learning modules Annalisa Baldi Modulo 1 Modulo 2.
27993 – ANALISI MATEMATICA T-2
Information on the course unit. My e-mail for students My e-mail for staff Close. First cycle degree courses. The language of mathematics, basics of logics and set theory.
The students are required to attend the lectures and to devote a right amount of time to autonomous study. The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function.
Analisi matematica – Michiel Bertsch, Roberta Dal Passo, Lorenzo Giacomelli – Google Books
The oral part of the exam must be passed in the same session of the written part. Absolute convergence of a series. Dal Passo e L. On-line material on IOL: The Cauchy problem for differential equations and systems.
ANALISI MATEMATICA T-2 / — University of Bologna
The evaluation of limits of one variable functions using both notable basic limits and Taylor’s formula. Planned learning activities and teaching methods:. Course Timetable from Feb 21, to May 03, Alternate series and Leibnitz criterion. Taylor’s formula of the second order for functions of several variables.
The detailed contents with the list of theorems and proofs, up to dated for each weak, can be found in the web course page. The course will provide tools, like integral calculus, number series and functions of two variables, that are used for courses on Probability and Statistics.
Generalities on real and vector functions of several real variables. The vector space structure, the dot product and the euclidean norm. The Weierstrass theorem and the intermediate value theorem for functions of several variables. The definition and the properties of the derivative of one variable functions. Conservative vector fields and their potentials. Theorems on existence, uniqueness and continuation of solutions.
The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit. Interior and constrained local extrema for real functions of several variables.
In the written part, lasting three hours, the solution of various exercises is required. The last one is of fundamental importance to develop the logic and practical abilities related with the topics covered in the course.
Partial derivatives of higher order. The course consists in hours of lectures, about one half of them is devoted to numerical and theoretical exercises. In matemafica period june-july the oral part may be passed in a subsequent session. Course Timetable from May 06, to Jun 07, The change of variables theorem for a double integral.
The flux of a vector field through an oriented surface. Pagani analusi Sandro Salsa, Analisi Matematica 1. The commission may require an oral examination in case the written one has not been sufficient for a clear grading. Double integrals on rectangular and normal domains computed by iterated integrals. Planned learning activities and teaching methods: Lessons are completed with examples and counterexamples illuminating the theoretical content. Outline of double improper integrals.
Smooth and piecewise smooth curves, length of a curve, integral of a function over a curve. Definition of a continuous function and of limit of a function.
The teacher will use, as far as possible, various technological tools to improve the learning and to let the students to have as much as possible education material to their disposal.
Definition of Riemann double integral for functions defined on a bounded and measurable set. Marco Bramanti, Esercitazioni di Analisi Matematica 1.
The divergence theorem and the Stokes theorem.
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Teaching methods The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables. Futhermore a lot of exercises are solved in the classroom. Partial derivatives, Schwarz theorem. Convergence criteria for numerical series. Department of Statistical Sciences. To this aim tutorial mwtematica will be organized and supervised by the teacher. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables.
Textbooks matemafica optional supplementary readings M.