Concept

Function of several real variables

Related lectures (23)

Real Functions: Definitions and Examples

Explores definitions and examples of real functions of a real variable.

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Real Functions of Several Variables: Definitions and Examples

Covers definitions and examples of real functions of several real variables, including limits and visualization techniques.

Real Functions: Continuity and Limits

Explores continuity and limits of real functions, including examples and the concept of uniform continuity.

Continuity and Limits in Multivariable Functions

Explores limits and continuity in multivariable functions, including level sets and limit existence.

Recurrence Method: Generalization and Differential Calculus

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Partial Derivatives: Higher Order and Applications

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Partial Derivatives: Examples

Explains the concept of partial derivatives through various examples involving functions of two variables.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Multiple Integrals: Defining Integrals of Functions in R^2

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

Real Functions of Several Variables

Covers the concept of limits for real functions of several variables and their demonstration using polar coordinates and change of variables.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Integral Calculus of Functions in Several Variables

Covers the integration of functions in several variables, Darboux sums, and Fubini's theorem on a closed box.

Limits of Functions in R^n

Explores limits of functions in R^n and the importance of understanding derivatives in multiple dimensions.

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Real Functions: Continuity Theorem

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Implicit Functions Theorem

Discusses the uniqueness of implicit functions solutions and surfaces described by equations.