SylabUZ
Course name | Mathematical Analysis 4 |
Course ID | 11.1-WK-MATP-MA4-S22 |
Faculty | Faculty of Exact and Natural Sciences |
Field of study | WMIiE - oferta ERASMUS |
Education profile | - |
Level of studies | Erasmus programme |
Beginning semester | winter term 2024/2025 |
Semester | 2 |
ECTS credits to win | 4 |
Course type | optional |
Teaching language | english |
Author of syllabus |
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The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
Lecture | 30 | 2 | - | - | Exam |
Class | 30 | 2 | - | - | Credit with grade |
To acquaint the student with the theory of smooth surfaces, the concept of orientation, and then the theory of non-oriented and oriented surface integral; Stokes theorems and their role in physics, as well as a brief overview of the concepts of divergence and rotation of a vector field.
Mathematical Analysis 1, 2 and 3; Linear Algebra 1 and 2; Logic and Set Theory
Lecture
I. Surfaces
Smooth surface (2 hours); tangents space (3 hours); measure on a smooth surface ( 2hours); Orientation and orientability of a smooth surface (3 hours)
II. Surface integrals
Unoriented surface integral (2 hours); Surface integrals of vector fields (3 hours), Greens theorem (3 hours); Independence of path (1 hour); Surface integral (3 hours); Gauss-Ostrogradsky theorem (3 hours); Stockes' Theorem (3 hours); Vector fields (2 hours)
Classes
I. Surfaces
Examples of smooth surfaces (3 hours); Tangent space (2 hours); Orientation and orientability of a smooth surface, Möbius strip (3 hours)
II. Surface integrals
Parametric description of the curve and surface (3 hours) Unoriented surface integral, Curve length (3 hours); Surface integrals of vector fields (3 hours), Greens theorem (3 hours); Independence of path (1 hour); Surface integral (3 hours); Gauss-Ostrogradsky theorem (2 hours); Stockes' Theorem (3 hours); Vector fields (2 hours); Line integrals (3 hours); Independence of the integral from the path of integration (3 hours); Application of Green's formula (2 hours); Vector field of divergence and rotation (2 hours)
Colloquium (2 godz.)
Traditional lecture; exercises in which students solve problems and discuss, as well as prepare biographies of mathematicians whose names appear at the lecture; group work completed with a written study; work with a book and with the help of the Internet. If necessary (determined by the order of the Rector of the University of Zielona Góra), classes can be in online form.
Outcome description | Outcome symbols | Methods of verification | The class form |
The grade for the subject is the arithmetic mean of the classes grade and the exam grade. The necessary condition for taking the exam is a positive grade from the classes. The necessary condition for passing the course is a positive grade from the exam.
Modified by dr Dorota Głazowska (last modification: 18-04-2024 13:08)