1. SylabUZ
2. Wydział Fizyki i Astronomii
3. semestr zimowy 2020/2021
4. Fizyka - pierwszego stopnia z tyt. licencjata
5. Algebraic and geometrical methods in physics

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Algebraic and geometrical methods in physics - opis przedmiotu

Cel przedmiotu

The main aim of course is to give students mathematical tools of algebra and analytic geometry necessary for their further studies of physics. Developing the ability to use algebraic and geometric tools for setting and solving physical problems. Use of vector mathematical tools such as vector space, linear transformation or Euclidean space.

Wymagania wstępne

Zapisz zmiany

Knowledge of mathematics and physics at the level of post-gymnasium

Zakres tematyczny

Lecture:

I. Complex numbers: Cartesian and polar parametrization. Complex roots, roots of unity.

II. Polynomials of one variable: operations on polynomials, division of polynomials with rest, roots of polynomials, fundamental theorem of algebra.

III. Matrices: operations on matrices, matrix classification. Square matrices: determinant and its properties. Methods of calculation of determinants.

Cramer linear systems and methods for solving them.

IV. Euclidean vector spaces: vectors in R^2, R^3 and R^n, vector components, vector operations, vector norms, scalar and vector product,, orthogonal vectors, angle between vectors.

V. Geometry of linear systems: vectors of solutions of systems of homogeneous and non-homogeneous linear equations.Order of a matrix, Kronecker-Capelli theorem. Methods of solving for general systems of linear equations. Linear transformations and their basic properties. Matrix of linear transformation, eigenvectors and eigenvalues

VI. Elements of analytical geometry: parametric equations of straight lines in R^2 and R^3, equations of planes in space,  equations of straight lines and planes with given various data, conics in Cartesian and polar systems,

Class:

Practical realization of the matter presented during lectures and enhancement of the calculus skills.

Metody kształcenia

Lecture: classical lecture

Class: solving of problems related to the subjects considered during lectures with applications in physics.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture: Positive passing of written exam

Class: Positive passing of all written tests.

Before taking the exam a student must gain positive grade during the class.

Total score: average rating of the exam and grade from the class.

Literatura podstawowa

[1] T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1, Oficyna Wydawnicza GiS, Wrocław 2011

[2] T. Jurlewicz, Z. Skoczylas, Algebra liniowa 2, Oficyna Wydawnicza GiS, Wrocław 2011

[3] T. Jurlewicz, Z. Skoczylas, Algebra i geometria analityczna, Oficyna Wydawnicza GiS, Wrocław 2011.

[4] R. Larson, Elmentary linear algebra, 8 edition, Cengage Learning, 2007

[5] S. Lipschutz, M. Lipson, Schaum's outlines. Linear algebra, 3 edition, 2001

[6] E. W. Swokowski, Calculus with analytic geometry, Prindle, Weber & Schmidt Publishers, Boston 1983.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr hab. Piotr Lubiński, prof. UZ (ostatnia modyfikacja: 03-06-2020 13:24)