1. Explain and relate basic results of differential calculus of several variables
2. Apply and interpret basic methods and skills of differential calculus of several variables
3. Demonstrate and apply basic skills of integral calculus of several variables
4. Explain the notion of convergence of series of numbers and functions and apply basic criteria for testing convergence
5. Demonstrate skills to solve basic types of ordinary differential equations
6. Create and solve mathematical model based on differential equations for engeneering problems
7. Show the ability for mathematical modelling and problem solving applying methods of mathematical analysis in engineering
8. Show the ability for mathematical expressing and logical reasoning

Lectures are held in two cycles, 6 hours per week.

Excercises are held one hour per week.

Teaching materials and homeworks are accessible on course webpage.

1. Euclidean space R^n; Curves in R^n; Tangent line on the space curve; Vector functions; Derivative of vector function; Functions of several variables.
2. Limit and continuity; Partial derivatives; Differential; Gradient; Tangent plane, Higher order derivatives; Schwartz theorem.
3. Derivative of composite function and chain rule; Derivative of implicit function; Directional derivative; Mean value theorem.
4. Integrals depending on the parameter; Taylor's formula; Second differential and quadratic forms. Local extrema.
5. Global extrema, Extrema of a function subject to constraints; Lagrange mutliplier, Least squares method.
6. Notion of differential equation, the field of directions, orthogonal and izogonal trajectories, Equations with separated variables; Linear differential equation; Exact differential equation.
7. Homogeneous equation; Bernoulli and Riccati equation, General first-order differential equations; Singular solutions, Numerical solving of differential equations; Euler's method; Taylor's method.
8. Midterm exam
9. Double integral; Change of variables; Polar coordinates; Applications.
10. Triple integral; Change of variables; Cylindrical and spherical coordinates; Applications.
11. Series of numbers; Convergence of series, necessary conditions, Series with positive terms; Criteria for convergence, comparison, D'Alambert's, Cauchy's, integral criterion, Series of real numbers, absolute, conditional and unconditional convergent series.
12. Power series, area of convergence and radius of convergence, representation of a function, Taylor and Maclaurin series; Application of Taylor series, Convergence of function series; Uniform convergence; Differentiation and integration of function series.
13. Higher order differential equations; Decreasing the order, Linear differential equation of the second order; Homogeneous and nonhomogeneous equation, Examples; Harmonic motion; Applications in physics and electrical engineering.
14. Higher order homogeneous equations, Finding the particular solutions, Solving equations using series.
15. Final exam