Analysis 3

Compulsory course. 4 credits.

Theory: 3 credits + Exercises : 1 credits

I. Overview

This course provides :

- The integrals with parameters and multiple integrals.

- The line integrals, surface integrals and Stokes’ s theorem.

II. Prerequisites

Analysis 1 and 2.

III. Contents

Chapter 1. Multiple integrals.

1.1. Riemann’s sum and integrable functions, Riemann integrals.

1.2. Iterated integrals and Fubini’s theorem.

1.3. Change of variables in multiple integrals.

Chapter 2. Line integrals

2.1. Integrals with parameters.

2.2. First order differential forms and line integrals.

2.3. Green’s theorem.

2.3. Mathematica for line integrals.

Chapter 3. Surface integrals.

3.1. Oriented surface in R³ and Surface integrals.

3.2. Stokes’ theorem.

3.3. Mathematica for surface integrals.

References

[1] M. I. Abell and J. P. Braschon, Mathematica by example, Academic Press, NewYork, 1997.

[2] R. A. Adams, Calculus : A complete course, Addison – Wesley, 1991.

[3] S. Lang, A second course in calculus, Addison – Wesley, 1968.

[4] W. Rudin, Principles of mathematical analysis, Mc Graw – Hill, 1964.

[5] S. Wolfram, Mathematica, Cambridge University Press, 1996.