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. |