COURSE DESCRIPTION

Course code

MAP1080

Kind of studies

common to all departments;

Course title

Elements of Vector Analysis

First name, surname and title of the lecturer/supervisor

Komisja programowa Instytutu Matematyki i Informatyki

First name, surname and title of the team's members

Lecturers of the Institute of Mathematics and Computer Science

Course structure

Form of class Lecture Problems classes Laboratory Project Seminar Number of points
Number of hours/week 1 1 2+2
Course grade based on Test Test

Prerequisites

Mathematical Analysis 1

Course description

Line integrals. Surface integrals. Elements of vector calculus. Applications of line integrals and surface integrals in physical and technical problems.

Lectures

Contents of particular hours Number of hours
1. Curves on plane and in space. Line integrals of scalar functions along curves (path integrals): Definition and basic properties. Reduction of line integral of a scalar function to single integral. 2
2. Applications of path integrals. Line integrals of vector fields: Definitions and basic properties.2
3. Reduction of line integral of a vector field to single integral. Independence of path. Green`s theorem.2
4. Applications of line integrals of vector fields. Surfaces. 2
5. Surface integrals of scalar functions: Definition and basic properties. Reduction of surfaces integral of a scalar field to double integral. Application of surface integrals of scalar functions.2
6. Surface integrals of vector fields: Definitions and basic properties. Reduction of surface integral of a vector fields to double integral.2
7. Elements of vector calculus. Stoke`s theorem. Divergence theorem.2
8. Applications of surface integrals of vector fields.1

Problems classes

Contents of particular hours Number of hours
1. Exercises illustrating the material presented during the lectures.15

Material for self preparation

Basic literature

1. W. Żakowski, W. Kołodziej, Matematyka, Cz. II, WNT, Warszawa 2003.
2. T. Trajdos, Matematyka, Cz. III, WNT, Warszawa 2005.
3. M. Gewert, Z. Skoczylas, Elementy analizy wektorowej. Teoria, przykłady, zadania, Oficyna Wydawnicza GiS, Wrocław 2004.

Additional literature

1. G. M. Fichtenholz, Rachunek różniczkowy i całkowy, T. III, PWN, Warszawa 2007.
2. W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, Cz. II, PWN, Warszawa 2006.
3. F. Leja, Rachunek różniczkowy i całkowy ze wstępem do równań różniczkowych, PWN, Warszawa 2008.
4. R. Nowakowski, Elementy matematyki wyższej, T. II, Wydawnictwo Naukowo Oświatowe ALEF, Wrocław 2000.
5. B. K. Pszczelin, Analiza wektorowa dla inżynierów, PWN, Warszawa 1971.

Conditions required for a student to pass the course

Positive result of the test.