Матан - 2 on Windows Pc

Theorems with proofs of mathematical analysis. Write exam to the max!

All questions:
1. Formulated. def. primitive. Formulated. properties of primitive and indefinite integral.
2. Decomposition proper rational fraction into partial fractions. Integration of partial fractions.
3. Formulated. properties were determined. integral. Doc. theorem on maintaining the definite integral sign of the integrand.
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7. Formulated. def. integral with variable upper limit. Doc. theorem on the derivative of the integral with respect to its upper limit.
8. Formulated. properties were determined. integral. Derive Newton-Leibniz formula.
9. Formulated. and Doc. theorem on integration by substitution for the definite integral.
10. Formulated. and Doc. theorem on integration by parts for definite integrals.
11. Formulated. properties were determined. integral. Integration of periodic functions, the integration of even and odd functions on symmetric with respect to the origin.
12. Formulated. def. improper integral of the 1st kind. Formulated. and Doc. test for convergence in inequality for improper integrals of the 1st kind.
13. Formulated. and Doc. limit sign comparison for improper integrals of the 1st kind.
14. Formulated. and Doc. sign of absolute convergence for improper integrals of the 1st kind.
15. Formulated. def. improper integral of the 2nd kind and signs of convergence of these integrals.
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21. Linear differential equations of the first order. Integration of linear inhomogeneous differential equations of the first order Bernoulli method (Method U * V) and Lagrange method (variation of an arbitrary constant).
22. Formulated. Cauchy's theorem on the existence and uniqueness of solutions of differential equations th n-th order. Integration of differential equations of n-th order, allowing reduction of order.
23. Formulated. Cauchy's theorem on the existence and uniqueness of solutions of linear differential equations th n-th order. Doc. properties of particular solutions of a homogeneous linear differential equation th n-th order.
24. Formulated. def. linearly dependent and linearly independent system of functions. Formulated. and Doc. theorem on the Wronskian of linearly dependent functions.
25. Formulated. def. linearly dependent and linearly independent system of functions. Formulated. and Doc. theorem on the Wronskian of linearly independent particular solutions of homogeneous linear differential equations th n-th order.
26. Formulated. and Doc. theorem on the existence of a fundamental system of solutions of linear homogeneous differential equations th n-th order.
27. Formulated. and Doc. theorem on the structure of the general solution of a homogeneous linear differential equation th n-th order.
28. Derive the formula Ostrogradskii-Liouville problem for linear differential equations th 2nd order.
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33. Particular solution of inhomogeneous linear differential-th equation with constant coefficients and the right part of the special form (which is quasipolynomial). Formulated. and Doc. Theorem imposing particular solutions.
34. The Lagrange method of variation of parameters to find a solution of the linear inhomogeneous differential equation 2-nd-order and out of relationships for varying variables.
35. Formulated. def. diff-th equation of n-th order, permitted the highest derivative, and to formulate the Cauchy problem for this equation. Describe a method for reducing this equation to the normal system of differential equations.
36. Formulated. Cauchy problem for the normal system of differential equations and the theory of the Cauchy problem of the existence and uniqueness of the solution of this problem. Describe a method of reducing the normal system to a single differential equation of higher order.
37. Formulated. def. first integral of the normal system of differential equations. Describe the methods for finding the first integrals and their application to solving a system of differential equations.
Integration formulas
Integrals with a square polynomial
Integrals trigonometry
Formula areas, volumes, arc lengths and surface areas