1. Matrices, systems of linear algebraic equations, Gaussian elimination method. 2. Inverse matrix, determinants. 3. Geometrical vectors in three dimensional Euclidean space, operations with vectors. 4. Applications of vector calculus in spherical trigonometry. 5. Vector space, basis, dimension, coordinates of a vector. 6. Eigenvalues and eigenvectors of a matrix. 7. Application of vector calculus in analytic geometry. 8. Real function of one real variable, explicit and parametric expression of a function. Basic properties of functions. Composite fuction and inverse function. Elementary functions (including inverse trigonometric functions and hyperbolic functions). 9. Polynomials and rational functions. 10. Sequences and their limits, limit and continuity of a function. 11. Derivative of a function, its geometrical and physical meaning, derivation rules. Derivative of a composite function and of an inverse function. Derivatives of elementary functions. 12. Derivatives of higher order, geometrical meaning of first order and second order derivatives for sketching the graph of a function, l Hospital's rule, asymptotes. 13. Properties of functions continuous on an interval. Basic theorems of differential calculus (the Rolle and Lagrange theorems). Differential of a function. Taylor's theorem. Derivative of a function given in a parametric form.

1. Geometrical vectors in E3, operations with vectors. 2. Applications of vector calculus in spherical trigonometry. 3. Vector space, base, dimension, coordinates of a vector. 4. Application of vector calculus in analytic geometry. 5. Matrices, systems of linear algebraic equations, Gaussian elimination method. 6. Inverse matrix, determinants. 7. Eigenvalues and eigenvectors of a matrix. 8. Real function of a one real variable, explicit and parametric expression of a function. Basic properties of functions. Composite and inverse functions. Elementary functions. 9. Polynomials and rational functions. 10. Sequences and theirs limits, limit and continuity of a function. 11. Derivative of a function, its geometrical and physical meaning, derivation rules. Derivative of a composite function and of an inverse function. Derivatives of elementary functions. 12. Derivatives of higher order, geometrical meaning of first and second order derivatives for investigation of behavior of a function, l`Hospitals rule, asymptotes. 13. Properties of function, continuous on an interval. Basic theorems of differential calculus. Differential of a function. Taylor’s theorem. Derivative of a function given in a parametric form. Primitive function, Newtons integral, its properties and computation. Riemann’s integral. Integration methods for indefinite and definite integrals.