The basics of differential and integral calculus of real-valued functions of several real variables, especially of real-valued functions of two real variables. Applications of local extrema in examples from the fields of chemistry and physics. Ordinary differential equations. First- and second-order linear differential equations with constant coefficients and their applications in physics and chemistry. Double integrals. Vector fields, line integrals of vector fields. Applications.

1. a) The basics of differential and integral calculus of real functions of several variables, especially of real functions of two variables (allocated 0/4)
b) Applications of local extrema in examples from the fields of chemistry and physics. (allocated 0/2)
c) Gradient, linearization, tangent plane. (allocated 0/2)

2. a) Ordinary differential equations. First- and second-order linear differential equations with constant coefficients. (allocated 0/6)
b) Applications of differential equations in physics and chemistry. (allocated 0/2)

3. Double integrals and their applications. (allocated 0/4)

4. a) Vector fields, line integrals of vector fields. (allocated 0/2)
b) Calculation methods of line integrals. (allocated 0/2)