S.V. Podkletnova

This lecture introduces line integrals, extending integration from intervals to curves. Two types are covered: scalar line integrals with respect to arc length and vector line integrals. Physical motivations include finding the mass of a wire with va…

This lecture introduces surface integrals, extending integration from curves to two-dimensional surfaces. Two main types are covered: scalar surface integrals for functions like mass density, and vector surface integrals (flux) for fields like fluid …

This practical class focuses on applying the chain rule to composite functions of several variables, finding derivatives of implicitly defined functions, and computing gradients and directional derivatives. The class includes theoretical review, fiv…

The lecture focuses on differential calculus for functions of several variables. It begins with the chain rule for differentiating composite functions, covering cases where arguments depend on one or multiple variables. Theory is supported by proofs …

This practical session is designed to reinforce the theoretical material from the first lecture on series. Students will practice calculating sequence limits and learn to determine the convergence of series through concrete examples. The main focus i…

This lecture opens a new section of the mathematical analysis course dedicated to the theory of series. Students will be introduced to the fundamental concepts needed to understand how infinite sums can lead to finite results. The first part thorough…

This lecture introduces functions of several variables, explaining the roles of independent and dependent variables, domain, and range. It covers methods for visualizing such functions, including graphs in three-dimensional space and level lines on a…

This lecture explores differentiability for functions of several variables. It begins by defining first-order partial derivatives, explaining that to compute them, all other variables are treated as constants. The geometric meaning is illustrated: a …

This practical class reinforces theoretical concepts through hands-on problem-solving. The session focuses on three key skills: finding domains of definition for functions with square roots, logarithms, and fractions by identifying constraints like n…

This practical class develops skills in differentiating functions of several variables. Students learn to compute first-order partial derivatives by treating all variables except one as constants. The session covers finding the total differential, w…

This practical class consolidates key concepts from the first two lectures. Students practice finding domains of definition by solving inequalities involving square roots, logarithms, and inverse trigonometric functions, then sketch the resulting reg…

This practical session focuses on applying line integral concepts through handsoll problem-solving. Students work through six problems covering scalar line integrals, work calculations, Green's Theorem applications, area computation using line integ…

This practical session focuses on applying surface integral concepts through hands-on problem-solving. Students work through seven problems covering scalar surface integrals, surface area calculation, flux integrals, Stokes' Theorem, and the Diverge…