Lectures
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I. Functions of one real variable
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Definition, graph and basic properties. Elementary functions. Operations with functions. Parametric and implicit functions. Limit of the function, continuous functions.
II. The calculus
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Definition of the derivative, basic rules for differentiation. Parametric differentiation, higher-order derivatives. Applications of the derivatives: tangent line, Taylor polynomial, extremes of a function,
behaviour of the graph (monotony, convexity, critical and inflection points), inverse functions,
computation of limits by l'Hospital rule, asymptotes.
III. Linear algebra and Analytic geometry
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Systems of linear equations, Gaussian elimination. Matrices, rank of a matrix. Matrix inversion, Determinant, its computation and properties. Cramer rule.
Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space.
Tutorials:
=================
1. Pre-calculus. simplifying of algebraic expressions, rules for computation of powers, exponentials, logarithms, solution of (in)equalities.
2. Domains of functions of one real variable.
3. Graphs and properties of elementary functions .
4. Differentiation: rules of computation (for any variable), simplifying, chain rule.
5. Analytic geometry in Euclidean space.
=================
I. Functions of one real variable
------------------------------------------------
Definition, graph and basic properties. Elementary functions. Operations with functions. Parametric and implicit functions. Limit of the function, continuous functions.
II. The calculus
------------------------------------------------
Definition of the derivative, basic rules for differentiation. Parametric differentiation, higher-order derivatives. Applications of the derivatives: tangent line, Taylor polynomial, extremes of a function,
behaviour of the graph (monotony, convexity, critical and inflection points), inverse functions,
computation of limits by l'Hospital rule, asymptotes.
III. Linear algebra and Analytic geometry
------------------------------------------------
Systems of linear equations, Gaussian elimination. Matrices, rank of a matrix. Matrix inversion, Determinant, its computation and properties. Cramer rule.
Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space.
Tutorials:
=================
1. Pre-calculus. simplifying of algebraic expressions, rules for computation of powers, exponentials, logarithms, solution of (in)equalities.
2. Domains of functions of one real variable.
3. Graphs and properties of elementary functions .
4. Differentiation: rules of computation (for any variable), simplifying, chain rule.
5. Analytic geometry in Euclidean space.