Lectures:
Real numbers and numerical sets. Supremum and infimum. Real functions of one real variable.
Elementary functions. Sequences of real numbers. Limit of a sequence. Limit of a function. Continuity of a function. Differential and derivative of a function.
Fundamental theorems of differential calculus. Taylor polynomial. Investigation of the behavior of functions.
Primitive functions and indefinite integral.
Methods of integration (integration by parts, substitution, partial fraction decomposition).
Integration of special classes of functions.
Riemann integral. Integral with a variable upper limit.
Computation of definite integrals.
Applications. Improper integrals.
Seminars:
Logical connectives and basic terms of propositional logic. Applications of the mathematical induction principle. Identification of supremum and infimum in various types of sets.
Definition of a function. Increasing, decreasing, periodic functions.
Injective functions, finding inverse functions. Graph representation of a function.
Applications of properties of elementary functions in solving equations and inequalities, and other problems.
Calculation of limits of sequences, discussion of the concept of limit of a function.
Techniques for computing limits of functions.
Computation of derivatives and differentials of functions.
Construction of Taylor polynomial and estimation of the remainder in function approximation. Applications of derivatives, differentials, and Taylor polynomial in physics, geometry, and numerical mathematics.
Solving problems on function behavior.
Solving problems from integral calculus using integration by parts and substitution methods.
Solving problems related to the decomposition of a rational fractional function into partial fractions.
Practice of special substitutions in the integration of certain classes of functions.
Computation of definite integrals. Applications.
Calculation of improper integrals. Use of convergence criteria for improper integrals.
Real numbers and numerical sets. Supremum and infimum. Real functions of one real variable.
Elementary functions. Sequences of real numbers. Limit of a sequence. Limit of a function. Continuity of a function. Differential and derivative of a function.
Fundamental theorems of differential calculus. Taylor polynomial. Investigation of the behavior of functions.
Primitive functions and indefinite integral.
Methods of integration (integration by parts, substitution, partial fraction decomposition).
Integration of special classes of functions.
Riemann integral. Integral with a variable upper limit.
Computation of definite integrals.
Applications. Improper integrals.
Seminars:
Logical connectives and basic terms of propositional logic. Applications of the mathematical induction principle. Identification of supremum and infimum in various types of sets.
Definition of a function. Increasing, decreasing, periodic functions.
Injective functions, finding inverse functions. Graph representation of a function.
Applications of properties of elementary functions in solving equations and inequalities, and other problems.
Calculation of limits of sequences, discussion of the concept of limit of a function.
Techniques for computing limits of functions.
Computation of derivatives and differentials of functions.
Construction of Taylor polynomial and estimation of the remainder in function approximation. Applications of derivatives, differentials, and Taylor polynomial in physics, geometry, and numerical mathematics.
Solving problems on function behavior.
Solving problems from integral calculus using integration by parts and substitution methods.
Solving problems related to the decomposition of a rational fractional function into partial fractions.
Practice of special substitutions in the integration of certain classes of functions.
Computation of definite integrals. Applications.
Calculation of improper integrals. Use of convergence criteria for improper integrals.