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# Educational- methodical complex on the Mathematics I

MY REFLECTIONS ON INTERCULTURAL COMPETENCE. To improve my knowledge of other cultures I find the following most effective:

Educational- methodical complex on the Mathematics I

Аstana

The course content

List of lectures

 The name of the theme hours Literature Current control, points 1. Determinants and their properties. Matrix. Operations with matrices. The inverse matrix. Systems of linear equations , 0,4 2. The simplest problem of analytic geometry. Equations of a straight line on a plane. , 0,4 3. Analytic geometry in space. Vectors. Simple operations with vectors. The scalar, vector and mixed product of vectors. , 0,4 4. The curves of the second order. Canonical equation of second order curves. , 0,4 5. Function. Methods of doing functions. The limit function. Fundamental theorems on limits. Infinitely small and infinitely large quantities. The ends. , 0,4 6. The derivative of the function. Geometric and mechanical meaning. Table of derivatives. The differential of a function. Derivatives of complex functions. , 0,4 7. Rolle's theorem, Lagrange, Cauchy. L'Hopital's rule. , 0,4 8. Investigation of the function. Extremum of the function. Necessary and sufficient conditions for the existence of an extremum. Convexity, concavity and inflection points. Assimptoty. The overall study of design features. , 0,4 9. Primitive. Indefinite integral and its properties. Table of integrals. Direct integration, integration with the change of variables, and by parts. , 0,4 10. Integration of simple rational fractions. Integration of rational fractions. , 0,4 11. Integration of expressions containing trigonometric functions. Integration of irrational functions. , 0,4 12. The definite integral. Problems leading to the definite integral. The Newton-Leibniz. , 0,4 13. Applications to the computation of the integrals of plane figures areas. Calculation the arc length, the amount of body rotation. The improper integral. , 0,4 14. Complex numbers. Complex numbers in trigonometric and exponential form. , 0,4 Total