Essentials of High School Math Course
Code  Completion  Credits  Range  Language 

01MAM  Z  2  0+2  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

Students are introduced to mathematical concepts and methods used in the introductory physics course.
 Requirements:

No prerequisities.
 Syllabus of lectures:

Coordinate systems, position (2D, 3D) (c.s. Cartesian, cylindrical, spherical,..), description of curves (conic,..). Translation, rotation around an axis.
Einstein summation convention, linear transformations, orthogonal transformations, matrices, operations with rows and columns of matrices, determinants, lin. vect. space (the existence of solutions, permittivity, permeability., flexibility, strength ...), eigenvectors, eigenvalues, matrix diagonalization, quadratic forms (moment of inertia)
Scalars  vectors  tensors, additive  the nonadditive quantity, size of units, field scalar x vector. Points, vectors, forms and operators. Scalar and vector products.
Differential calculus: total, partial derivatives, curve length, curvature. Derivatives of elementary functions, derivative of product and composite functions. Functions of several variables, differential. (speed, acceleration).
Introduction to integral calculus, Rieman integral, geometric and physical meaning. Differential equations (differential eq.  numerical solution)
Approximate solutions, series, limits, approximation of functions, Taylor expansion of function (approximation for the general potential, LHO)
Complex numbers, the Euler's formula, the Moivre's formula (oscillations, ..)
The geometry of curves  the distance, tangent vector, normal, osculating circle, the radius of curvature. Description of the area, interior space coordinates, normal. (normal and tangential acceleration)
Vector field: differential operator nabla, Laplace operator, operations with operators Gauss., Stokes. theorem, geometric meaning (potential energy, conservative force, work around a closed curve)
Basis: 2D 3D ND Continuous, Fourier Transform
Mechanics of continuous media, systems of partial differential equations (continuity equation, equation, perturbation, perturbations, dispersion relations, ..)
Functional, strength, other ways to determine the trajectory, the calculus of variations
Statistics, probability distribution function
 Syllabus of tutorials:

Coordinate systems, position (2D, 3D) (c.s. Cartesian, cylindrical, spherical,..), description of curves (conic,..). Translation, rotation around an axis.
Einstein summation convention, linear transformations, orthogonal transformations, matrices, operations with rows and columns of matrices, determinants, lin. vect. space (the existence of solutions, permittivity, permeability., flexibility, strength ...), eigenvectors, eigenvalues, matrix diagonalization, quadratic forms (moment of inertia)
Scalars  vectors  tensors, additive  the nonadditive quantity, size of units, field scalar x vector. Points, vectors, forms and operators. Scalar and vector products.
Differential calculus: total, partial derivatives, curve length, curvature. Derivatives of elementary functions, derivative of product and composite functions. Functions of several variables, differential. (speed, acceleration).
Introduction to integral calculus, Rieman integral, geometric and physical meaning. Differential equations (differential eq.  numerical solution)
Approximate solutions, series, limits, approximation of functions, Taylor expansion of function (approximation for the general potential, LHO)
Complex numbers, the Euler's formula, the Moivre's formula (oscillations, ..)
The geometry of curves  the distance, tangent vector, normal, osculating circle, the radius of curvature. Description of the area, interior space coordinates, normal. (normal and tangential acceleration)
Vector field: differential operator nabla, Laplace operator, operations with operators Gauss., Stokes. theorem, geometric meaning (potential energy, conservative force, work around a closed curve)
Basis: 2D 3D ND Continuous, Fourier Transform
Mechanics of continuous media, systems of partial differential equations (continuity equation, equation, perturbation, perturbations, dispersion relations, ..)
Functional, strength, other ways to determine the trajectory, the calculus of variations
Statistics, probability distribution function
 Study Objective:

Knowledge: learn the basic procedures for solving of simple physical problems
Abilities: applying of new abstract concepts on the description and solution of real physical situations and phenomena
 Study materials:

Povinná literatura: [1] Kvasnica J.: Matematický aparát fyziky, Academia, Praha, 1989, 1997
Doporučená literatura: [2] Mathematical Physics, Sadri Hassani, Springer 2000, ISBN 9780387985794
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: