MATHEMATICAL ANALYSIS II COURSE

Course objectives

Knowledge and understanding. Good theoretical and practical knowledge of differential calculus and integration for functions of several real variables. Ability to understand these issues also in the context of other courses. Applying knowledge and understanding. Ability to use the acquired skills for solving simple problems and for their use required in other courses. Making judgements. Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned. Communication skills. Good presentation skills of basic concepts and techniques of Mathematical analysis. Learning skills. Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Channel 1
GIULIA ROTUNDO Lecturers' profile

Program - Frequency - Exams

Course program
Basic notions of R^n topology. Real functions of 2 or more real variables. Limits and continuity. Differential calculus in several variables: partial derivatives, gradient and directional derivatives. Differentiability. Partial derivatives of higher order. Taylor's formula. Double and triple integrals: reduction method, change of variables. Generalized multiple integrals. Parametric integrals: continuity and derivation under the integral sign. Ordinary differential equations: first order equations with separable variables, first order linear equations. Second order linear equations with constant coefficients. Free optimization. Constrained optimization. Convex functions. Examples and applications of the topics studied.
Prerequisites
Linear Algebra; Calculus I
Books
-ANALISI MATEMATICA 2. EDIZ. MYLAB. CON CONTENUTO DIGITALE PER DOWNLOAD E ACCESSO anichini giuseppe; conti giuseppe; spadini marco (Pearson) -Teaching notes
Frequency
In person is adviced, although not mandatory.
Exam mode
Test: first a written test. If the written test is sufficient (mark>=18), then the student has to pass an oral test. During the course a mid-term and a final partial tests are foreseen. Whether 1) the mark in each of them is >= 12 and 2) the average is >=18 then the student has the right to access to the oral test in the exams of January and February. A student can decide to attend a regular written test, but if it is delivered for the correction, any mark of mid and final partial tests is going to be cancelled. A student passing the test in January may decide to give the oral exam either in January or in February. A student passing the test in June may decide to give the oral exam either in June or July. The time of the written test is about two hours. The exercises are of the kind shown at the lesson and reported on Moodle (elearning Sapienza). A document is needed to attend the tests. No support is admitted (no books, no devices).The minimum to pass a written test is 18. The subjects of the oral test span on all the materials of the lessons.
Lesson mode
Classroom teaching.
  • Lesson code10612163
  • Academic year2024/2025
  • CourseStatistics, Economics, Finance and Insurance
  • CurriculumFinanza e assicurazioni
  • Year2nd year
  • Semester1st semester
  • SSDMAT/05
  • CFU6
  • Subject areaMatematico