Mathematics 2

This course aims to develop understanding in basic concepts of mathematical analysis. The course introduces concepts and applications of indefinite, definite and double integrals, types of series and their convergence tests, the basics of interpolation, complex numbers, Euclidean algorithm, concepts and solution methods of the first and second order differential equations.

This course aims to develop understanding in basic concepts of mathematical analysis.

Mathematics 1

1. The concept of indefinite integral. Direct integration. Integration by substitution. Integration by parts. Integration of rational functions. Integration of trigonometric functions. 2. Area of a curvilinear trapezoid and the concept of definite integral. Properties of the definite integral. Newton–Leibniz formula. Integration by substitution for definite integrals. Integration by parts for definite integrals. Applications of definite integral. Numerical integration. 3. Double integrals. 4. Algebraic form and operations of complex numbers. Trigonometric form and operations of complex numbers. Exponential form and operations of complex numbers. 5. Convergence of number series. Necessary condition for the convergence. Sufficient conditions for the convergence of the positive number series. Alternating series. Absolute convergence. Interval of convergence of the power series. Representation of functions as power series. Maclaurin and Taylor series. 6. Basic concepts of differential equations. First order differential equations with separable variables. First order homogeneous equations. First order linear equations.

1. Is able to recognize and describe the concepts of integrals, to choose appropriate solution methods for integration Is able to calculate determinant and rank of different order matrix. 2. Is able to apply definite integral for calculation of area under curves and arc length. 3. Demonstrates the knowledge to recognize and describe the concepts of series, to set convergence intervals, to calculate sum of series, to choose appropriate method for series convergence investigation. 4. Clearly defines the differences between forms of complex numbers, performs operations with complex numbers. 5. Is able to recognize and describe the concepts of differential equations, choose appropriate solution methods to solve first and second order differential equations.