Автор: S.V. Podkletnova
Practical Class 4. Differentiation of Composite Functions
S.V. Podkletnova
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,...
Lecture 3. Differentiation of Composite and Implicit Functions
S.V. Podkletnova
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...
Practical Session 2: Surface Integrals and Advanced Theorems
S.V. Podkletnova
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...
Practical Session 1: Line Integrals and Related Theorems
S.V. Podkletnova
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...
Practical Class 3: Functions of Several Variables: Limits and Differentiation
S.V. Podkletnova
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...
Practical Class 2. Differentiation of Functions of Several Variables
S.V. Podkletnova
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...
Lecture 2. Differentiability of Functions of Several Variables and Partial Derivatives
S.V. Podkletnova
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...
Lecture 1. Introduction to the Analysis of Functions of Several Variables
S.V. Podkletnova
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...
