Part 1 - Linear Algebra
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* Systems of linear equations - basic concepts, equivalent systems of equations, Gauß elimination, Frobenius Theorem, the solvability of systems of linear equations; analytic geometry in affine spaces A2, A3 and Euclidean spaces E2, E3 - basic affine concepts, line and plane equations; vector spaces with scalar multiplication, norm of general vectors, mutual position of planes, lines and their combinations; the distance of a point from a line or plane in E2 and E3.
Part 2 - Introduction to integral calculus
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* Antiderivative of functions - definitions and basic concepts, rules of integration, integrations by parts.
* Antiderivative of functions - integration by substitution (transformations of integrals), integration of basic rational, irrational and goniometric functions.
* The definite integral, properties of the Riemann integral, Newton-Leibniz' formula, geometric application of Riemann integral (computation of area-largeness).
* The definite integral - definition of improper integral, basic properties.
Part 3 - Introduction to differential calculus of two variables
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* Functions of two variables - basic concepts, the domain of real functions of two real variables and their visualisation; graph of a function and its visualisation.
* Functions of two variables - partial derivatives of first and higher orders; tangent plane, total differential of a function and its basic applications.
* Functions of two variables - local extrema and basic optimization methods (unconstrained optimization).
* Functions of two variables - constrained optimization (elimination of variables, the method of Lagrange multiplier).
Part 4 - Ordinary differential equations (ODE)
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* 1st-order ODE - basic concepts, general solution, particular solution; solving ODE by separation and integration; linear differential equations with non-constant coefficients, variation of constant.
* 2nd-order ODE - 2nd-order linear differential equations with constant coefficients and special RHS, solution estimation.
Part 5 - Ordinary difference equations
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* Introduction to difference calculus - basic concepts, general and particular solution, 1st-order linear difference equation with constant coefficients and special RHS, solution estimation.
* Introduction to difference calculus - 2nd-order linear difference equation with constant coefficients and special RHS, solution estimation.
Part 6 (formally)
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Revision of the previous concepts and their interrelationship.
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* Systems of linear equations - basic concepts, equivalent systems of equations, Gauß elimination, Frobenius Theorem, the solvability of systems of linear equations; analytic geometry in affine spaces A2, A3 and Euclidean spaces E2, E3 - basic affine concepts, line and plane equations; vector spaces with scalar multiplication, norm of general vectors, mutual position of planes, lines and their combinations; the distance of a point from a line or plane in E2 and E3.
Part 2 - Introduction to integral calculus
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* Antiderivative of functions - definitions and basic concepts, rules of integration, integrations by parts.
* Antiderivative of functions - integration by substitution (transformations of integrals), integration of basic rational, irrational and goniometric functions.
* The definite integral, properties of the Riemann integral, Newton-Leibniz' formula, geometric application of Riemann integral (computation of area-largeness).
* The definite integral - definition of improper integral, basic properties.
Part 3 - Introduction to differential calculus of two variables
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* Functions of two variables - basic concepts, the domain of real functions of two real variables and their visualisation; graph of a function and its visualisation.
* Functions of two variables - partial derivatives of first and higher orders; tangent plane, total differential of a function and its basic applications.
* Functions of two variables - local extrema and basic optimization methods (unconstrained optimization).
* Functions of two variables - constrained optimization (elimination of variables, the method of Lagrange multiplier).
Part 4 - Ordinary differential equations (ODE)
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* 1st-order ODE - basic concepts, general solution, particular solution; solving ODE by separation and integration; linear differential equations with non-constant coefficients, variation of constant.
* 2nd-order ODE - 2nd-order linear differential equations with constant coefficients and special RHS, solution estimation.
Part 5 - Ordinary difference equations
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* Introduction to difference calculus - basic concepts, general and particular solution, 1st-order linear difference equation with constant coefficients and special RHS, solution estimation.
* Introduction to difference calculus - 2nd-order linear difference equation with constant coefficients and special RHS, solution estimation.
Part 6 (formally)
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Revision of the previous concepts and their interrelationship.