Схема розділу
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Objective: To learn the concepts of primitive and indefinite integrals. To study the table of basic indefinite integrals and simple rules of integration.
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Objective: To learn how to apply variable substitution when finding indefinite integrals.
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Objective: To learn how to isolate the whole part from an improper fraction, integrate elementary fractions, and decompose proper rational fractions into elementary ones.
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Objective: Learn how to find typical trigonometric integrals by applying trigonometric transformations and variable substitution. Learn how to integrate linear irrationalities.
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Objective: To learn the concept of a definite integral and its main properties. To learn how to calculate definite integrals using Newton-Leibniz formula, substitution of variables, and integration by parts.
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Learn to apply the definite integral to find the areas of plane figures, the arc length of a curve and the volume of figures of revolution
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To master the concept of the double integral. Learn to reduce the double integral in Cartesian coordinates to a repeated integral.
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To master the concept of the triple integral. Learn to find the triple integral in Cartesian coordinates to the repeated integral.
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To master the concepts of the curvilinear integral of the first and second kind. Learn to find curvilinear integrals with different ways of setting the curve.
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Objective: To learn the general concepts of differential equations, to learn how to solve the main types of first-order differential equations.
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Objective: to learn how to solve typical differential equations that allow for a reduction in order
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Objective: To learn how to find a general solution to linear homogeneous differential equations for different cases of roots of the characteristic polynomial. To learn how to solve linear non-homogeneous differential equations in the case of a special right-hand side.
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Objective: To learn the basic concepts of numerical series and the necessary condition for convergence of a series.
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Objective: To learn the properties of alternating series and apply Leibniz's rule.
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Objective: To learn the basic concepts of functional series, properties of power series, and how to expand functions into Taylor series.
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To become familiar with the basic concepts of probability theory and mathematical statistics