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Course, academic year 2018/2019
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Seminar on Mathematical Methods of Physics - NOFY002
Title in English: Proseminář z matematických metod fyziky
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015
Semester: winter
E-Credits: 2
Hours per week, examination: winter s.:0/2 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Pavel Krtouš, Ph.D.
doc. RNDr. Jiří Langer, CSc.
RNDr. Robert Švarc, Ph.D.
Classification: Physics > General Subjects
Annotation -
Last update: T_UTF (02.05.2001)
Mathematical methods used in the introductory physics course.
Aim of the course -
Last update: T_KVOF (28.03.2008)

Mathematical methods used in the introductory physics course.

Course completion requirements - Czech
Last update: prof. RNDr. Pavel Krtouš, Ph.D. (12.10.2017)

Zápočet se uděluje za účast. Nedostatečná účast nelze nahradit jiným způsobem.

Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Kvasnica J.: Matematický aparát fyziky, Academia, Praha, 1989

Syllabus -
Last update: prof. RNDr. Pavel Krtouš, Ph.D. (25.09.2006)
Vectors and vector operations.
Columns, rows and matrices. Points, vectors, forms and operators. Scalar and vector product.

Geometry and motion in Euclidian space
Distance. Isometries of Euclidian space. Geometry of curves and surfaces. Velocity and acceleration in inercial and noninercial frames.

Differential calculus.
Derivative of elementery functions. Leibniz rule. Functions of many varibles. Total diferential.

Integral calculus
Geometrical and physical meaning of the Riemann integral, methods of integration. Volume and surface integrals.

Differential equations
Solution of the differential equation, existence and uniqueness of the solution. The first inegral, integral of energy. The solution of systems of linear differential equations by the separation of variables.

Differential operators.
Gradient, divergence, curl, Laplace operator and their geometric and physical meaning. Gauss and Stokes theorems

Tensors.
Definition of a tensor, coordinates of tensors and their physical meaning.

 
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