1. Notion of a primitive function. Properties of an indefinite integral. Integration methods for indefinite integral. 2. Integrating a rational function. Integrating a trigonometric function. 3. Integrating selected types of irrational functions. Newton integral, its properties and calculation. Riemann integral. 4. Applying calculus in geomery and physics. 5. Real functions two and more variables, composite functions. Limit and continuity of functions two and more variables. Theorems on continuous functions. 6. Partial derivatives, partial derivatives of a composite function, higher-order partial derivatives. Transformations of differential expressions. 7. The total differential of a function. Higher-order total differentials. Taylor polynomial of a two-function. Local maxima and minima of two-functions. 8. Functions defined implicitly. Two-functions defined implicitly. 9. Global maxima and minima. Simple problems in global maxima and minima using relative maxima and minima. Scalar field and its levels. Directional derivative of a scalar function, gradient. 10. Tangent and normal plane to a 3D curve. Tanget plane and normal to a surface defined explicitly.

1. Integrating a rational function. 2. Integrating a trigonometric function. 3. Integrating selected types of irrational functions. Newton integral, its properties and calculation. Riemann integral. 4. Geometric and physical applications of calculus. 5. Real functions of two and more variables, composite function. Limit and continuity. 6. Seminar test I. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Transformations of differential expressions. 7. The total differential of a function. Higher-order total differentials. Taylor polynomial of functions of two variables. Local extreme of functions of two variables. 8. Functions defined implicitly. 9. Seminar test II. Global extreme. Scalar field and its levels. Directional derivative of a scalar function, gradient. 10. Tangent and normal plane to a 3D curve. Tangent plane and normal to a surface defined explicitly.