### Mathematical Analysis II

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Syllabus: Topological notions.

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Domain, set level, limit and continuity of scalar and vector fields. Differential calculus in IRn: Directional and partial derivative. Chain rule. Differential operators: gradient, divergence and curl.

## MATHEMATICAL ANALYSIS II

Maximum and minimum values of a scalar field. Parameterizations of lines; Line integrals of scalar and vector fields. Conservative fields. Parameterizations of surfaces; Surface integral of scalar and vector fields.

## Math 412 - Mathematical Analysis II

Search in unipg. Reference texts The main material introduced during lectures and is contained in Text-book: 1 C. Other recommended books: M. Esculapio, Bologna, AMAR, A.

Esculapio, Prerequisites This course assumes that the student has a good working knowledge of Mathematical Analysis I topics including limits, continuity, derivatives, basic integration and improper integrals on the real line. These prerequisites are concepts that students meet not only in the mentioned basic course of Mathematics but also in their pre-university education.

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## Mathematical Analysis II

Teaching methods The course is split into traditional lectures face-to-face lessons on all the arguments of the course in which several exercises are presented to the students. In addition to a detailed theoretical expositions, for each argument the teacher will illustrate the relative exercises, which will be the model for the ones proposed in the written exam.

Some advices for to study the course, the book text and the exam tests: 1. Read the example problems carefully, completing some steps that are left out ask someone for help if you can't follow the solution to a worked example.

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Later use the worked examples to study by covering the solutions, and seeing if you can solve the problems on your own. Keep in mind that sometimes an answer could be expressed in various ways that are analitically equivalent, so don't assume that your answer is wrong just because it doesn't have exactly the same form as the answer in the back. Other information The course lasts 63 hours fase to fase. Attendance of the lectures is warmly recommended. Tutorial service is given in office hours.

Customiced consulting students. It's desidered a tutorial activity. The lectures will be companied by exercises sessions. The teacher will distribute educational material on the argument : Lebesgue integration in italian useful for a better understanding of this topic. Some tips: Don't miss class. Ask questions. Prerequisites for the course are the previous three semesters of the education in either Mathematics or Mathemtics-Economics.

In particular the course Mathematical Analysis 1 is essential. The first text is the one used for the course Mathematical Analysis 1.

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The second text is here , and will also be available in a printed version. They are referred to as [PF] and [AJ], respectively. The exam is a four hour written exam.

The syllabus and information about the exam are given here. Infinite series. Review of convergence and divergence. Sequences and series of functions.

See Summary 1. Uniform convergence of sequences of functions. Power series. See Summary 2.