Syllabus of lecture
Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions.
Integration by substitutions, integration by parts.
Integration of rational functions.
Definite integral and methods of integration.
Geometric and physical application of definite integrals.
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.
Total differential of functions of two variables, tangent plane and normal to a surface, derivation of implicit functions.
Extrema of functions.
Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations.
Linear differential equations of the first order, method of variation of arbitrary constant. Exact differential equations.
2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian, fundamental system of solutions.
2nd order LDE with constant coefficients - method of variation of arbitrary constants.
2nd order LDE with constant coefficients - method of undetermined coefficients.
Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions.
Integration by substitutions, integration by parts.
Integration of rational functions.
Definite integral and methods of integration.
Geometric and physical application of definite integrals.
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.
Total differential of functions of two variables, tangent plane and normal to a surface, derivation of implicit functions.
Extrema of functions.
Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations.
Linear differential equations of the first order, method of variation of arbitrary constant. Exact differential equations.
2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian, fundamental system of solutions.
2nd order LDE with constant coefficients - method of variation of arbitrary constants.
2nd order LDE with constant coefficients - method of undetermined coefficients.