ІІ етап Всеукраїнської студентської олімпіади з «Математики» 2016/2017

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MATHEMATICAL ANALISIS    (group ІН-45а)

THEORETICAL QUESTIONS FOR EXAM
1 SEMESTRE 


1.    Limit of the function. Limit at infinity. Definition.   L3, V2 p.29, 37-39, 43-49
2.    Limit at real point. Definition.   L3 ,V2 p.27-29, 33-37, 39-43                                                 
3.    Basic theorems concerning arithmetical operations for the limit. L3, V2 p.27
4.    1-st fundamental limit.  L4 ,V2 p.31, 49
5.    2-nd fundamental limit.  L4, V2 p.31,51-63
6.    Infinitesimals and main properties. Comparison of two infinitesimals values.L4, V2 p.23-25, 
7.    Equivalent infinitesimals. Using equivalent infinitesimalsfor calculation of the limits. L4, V2 p. 63-67
8.    One-sided limits. Left limit, right limit. Definition.   L3, V2 p.29
9.    Continuity of the function. Definition.  L5, V2 p.67-69
10.    Points of discontinuity and their kind.  L5 ,V2 p.69-75
11.    Derivative. Definition. The elementary rules of derivatives calculation. L6, V2 p.127-129,  131
12.    The derivative of the composite function.   L6 ,V2 p.129,131-133
13.    The physical meaning of the derivative.  L6, V2 p.
14.    Differentiation of implicit function.  L6 ,V2 p.133-135
15.    The logarithmic differentiation. L6, V2 p.135-137
16.    Differentiation of the function given in a parametric form.   L6 ,V2 p.141
17.    The geometric meaning of the derivative. L6 ,V2 p.137-139
18.    The equations of the tangent and the normal line.L6, V2 p.137-139
19.    Differential of the function.  L6, V2 p.139-141
20.    The application of the differential to approximate calculations.L6, V2 p.143
21.    Derivatives of the higher orders.   L6 ,V2 p.143-145
22.    L`Hospital`s rule. L7, V2 p.149-159
23.    Condition of the function monotonicity. L9 ,V2 p.163,165-167
24.    Extremum of the function.The necessary condition for existence of an extremum. The sufficient condition for existence of an extremum.L9, V2 p.163, 165-167
25.    Convexity and concavity of the curve. Points of inflection.L9, V2 p.167-169, 169-173
26.    The necessary condition for existence of an inflection point. The sufficient condition for existence of an inflection point.L9, V2 p.169,
27.    Asymptotes of the curve. L9 ,V2 p.173-175
28.    Vertical asymptote. L9, V2 p.173-175
29.    Inclined asymptote. Horizontal asymptote.L9 ,V2 p.175,177
30.    Antiderivative. Indefinite integral. Basic properties. L10, V2 p.251
31.    Table of integrals. L10 ,V2 p.251-253
32.    Methods of integration. Integration by substitution (change of variable). L10, V2 p.253-263,265-267
33.    Method of integration by parts.L10 ,V2 p.287-299
34.    Integration of rational functions.The partial fractions. Integration of the partial fractions. L10 ,V2 p.301-323
35.    Integration of trigonometric functions. L10, V2 p.323-335,335-343
36.    Integration of irrational expressions. L10, V2 p.267-281