KAG/KMA4 Mathematical Analysis 4

Seminar lecturers: Pavel Calábek, Jaroslav Švrček
Seminar: 12 hours/semester
Credits: 5
Summer semester
Form of course completion: course credit, exam

• Differential calculus in R^n: Partial derivatives and directional derivatives in R^n. Partial derivatives of higher order, interchanging the order of differentiation, total differential of a function and its application in approximate computing. Partial derivatives of compound functions. Differentials of higher order. The Taylor formula. Local extrema of functions, global extrema.
• Implicit functions: Implicit functions of a single variable, its existence, uniqueness and differentiability. Extrema of implicit functions. Implicit functions of several variables. Constraint extrema, method of the Lagrange multipliers.
• Integral calculus in R^n: The Jordan measure of a set in R^n. Properties of the measure. Definition and fundamental properties of the Riemann integral in R^n, its geometric interpretation. Multiple integration over intervals and normal domains. Substitution in integrals, especially polar, cylindrical and spherical coordinates. Practical aplications.