Mathematical analysis 2

Dr. Vesna Manova Erakovik, Professor

Msc Stevo Gjorgjiev, Assistant

Course content:

I. Functions of one variable: 1. Indefinite integral: Definition and properties; Shift in indefinite integral; Partial integration; Integrating rational, irrational and trigonometric expressions. 2. Definite integral: Definition and properties; Darbou's sums; Newton-Leibniz formula; Improper integrals; Application. 3. Rows: Number of rows; Convergence criteria; Functional arrays; Functional rows; Power lines.

II. Functions of several variables: 4. Notion of a function of several variables; Limit value of a function; Continuity of function. 5. Differentiation: Partial derivatives; Differentiability of a function at a point; Tangent plane and surface normal; Differentials of higher order and Taylor's formula; Local extremes; Conditional extremes. 6. Integrating: Double integrals over an arbitrary area; Surface integrals of the first and second type; Curvilinear integrals of the first and second type; Green's Formula; Triple integrals; Application.

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