1. define and explain basic notions of discrete mathematics
2. apply basic counting methods in combinatorics
3. explain and relate fundamental notions and results of differential calculus
4. demonstrate and apply methods and techniques of differential calculus
5. describe and relate fundamental notions and results of integral calculus
6. demonstrate and apply techniques of integral calculus
7. demonstrate ability for mathematical modeling and problem solving
8. use critical thinking
9. demonstrate ability for mathematical expression and logic thinking
10. use methods of mathematical analysis in engineering

Lectures are held in two cycles, 6 hours per week.

Excercises are held two hours per week.

Teaching materials and homeworks are accessible on course webpage.

1. Integers and rational numbers. Set of real numbers, Order in set of real numbers, absolute value, inequalities, infimum and supremum, Complex numbers, arithmetic operations, trigonometric form, powers and roots of complex numbers, Sets. Subsets. Set algebra. Direct product of sets, Integers. Mathematical induction
2. Real functions. Injection, surjection, bijection. Composition. Inverse function, Bijective functions. Equipotent sets. Cardinal number, countable and uncountable sets, Binary relations. Equivalence relation. Quotient set
3. Permutations, variations and combinations (without or with repetitions), Binomial and multinomial theorem. Inclusion-Exclusion principle, Pigeonhole principle, Generating functions. Operations with generating functions. Applications in enumerative combinatorics
4. Elementary functions, properties and basic relations, graphs, Graph transformations, translation, symmetry, rotation, Parametric functions. Polar equations of the plane curves
5. Sequences, subsequences, accumulation points. Limit, convergence of a sequence, Monotone sequences, some notable limits
6. Limit of a function, properties and operations with limits, One-sided limits. Limits of indeterminate forms, Continuity of functions. Properties of function on interval
7. Derivative of a function, geometrical and physical interpretation, differentiation rules, Derivative of composition and inverse function. Higher order derivatives, Differentiation of elementary functions
8. Midterm exam
9. Differentiation of implicit and parametric functions, Basic theorems of differential calculus, Lagrange mean value theorem, Taylor's theorem, Taylor's polynomial, L'Hospital's rule. Limits of indeterminante forms
10. Tangent and normal lines to the graph of function. Increasing and decreasing functions, Convexity and concavity of a function. Finding extrema of a function, necessary and sufficient conditions
11. Asymptotes. Qualitative graph of a function, Differential of an arc. Curvature. Evolute, Area under a curve, definite integral, Newton-Leibniz formula
12. Methods of integration, substitution, integration by parts, Integration of rational functions, Integration of trigonometric functions
13. Improrer integrals, Area of planar sets
14. Arc length of curves, Volume of solid of revolution, Area of sets and length of curves in polar coordinates, Surface of solid of revolution, Application of integrals in physics
15. Final exam