Syllabus of lecture
1. Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary
functions.
2. Integration by substitutions, integration by parts.
3. Integration of rational functions.
4. Definite integral and methods of integration.
5. Geometric and physical application of definite integrals.
6. Differential calculus of functions of two or more real variables. Functions of two or more variables, graph,
partial derivatives of the 1-st and higher order.
7. Total differential of functions of two variables, tangent plane and normal to a surface, derivation of implicit
functions.
8. Extrema of functions.
9. Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations.
10. Linear differential equations of the first order, method of variation of arbitrary constant. Exact differential
equations.
11. 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian,
fundamental system of solutions.
12. 2nd order LDE with constant coefficients - method of variation of arbitrary constants.
13. 2nd order LDE with constant coefficients - method of undetermined coefficients.
14. Reserve.
Syllabus of tutorial
1. Course of a function of one real variable.
2. Integration by a direct method. Integration by substitution.
3. Integration by substitution. Integration by parts.
4. Integration of rational functions.
5. 1st test (basic methods of integration). Definite integrals.
6. Applications of definite integrals.
7. Functions of more variables, domain, partial derivatives.
8. Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions.
9. Extrema of functions. 2nd test (functions of two variables).
10. Differential equations, separable and homogeneous differential equations.
11. Linear differential equations of 1st order. Exact differential equations.
12. 2nd order linear differential equations with constant coefficients.
13. Method of undetermined coefficients. 3rd test (differential equations).
14. Reserve.
1. Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary
functions.
2. Integration by substitutions, integration by parts.
3. Integration of rational functions.
4. Definite integral and methods of integration.
5. Geometric and physical application of definite integrals.
6. Differential calculus of functions of two or more real variables. Functions of two or more variables, graph,
partial derivatives of the 1-st and higher order.
7. Total differential of functions of two variables, tangent plane and normal to a surface, derivation of implicit
functions.
8. Extrema of functions.
9. Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations.
10. Linear differential equations of the first order, method of variation of arbitrary constant. Exact differential
equations.
11. 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian,
fundamental system of solutions.
12. 2nd order LDE with constant coefficients - method of variation of arbitrary constants.
13. 2nd order LDE with constant coefficients - method of undetermined coefficients.
14. Reserve.
Syllabus of tutorial
1. Course of a function of one real variable.
2. Integration by a direct method. Integration by substitution.
3. Integration by substitution. Integration by parts.
4. Integration of rational functions.
5. 1st test (basic methods of integration). Definite integrals.
6. Applications of definite integrals.
7. Functions of more variables, domain, partial derivatives.
8. Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions.
9. Extrema of functions. 2nd test (functions of two variables).
10. Differential equations, separable and homogeneous differential equations.
11. Linear differential equations of 1st order. Exact differential equations.
12. 2nd order linear differential equations with constant coefficients.
13. Method of undetermined coefficients. 3rd test (differential equations).
14. Reserve.