Modeling Heat Equation

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Related lectures (28)

Page 3 of 3

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Differentiability in Analysis

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Partial Differential Equations: Basics and Classification

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.

Partial Derivatives: Gradient and Theorem of Mean Value

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Partial Derivatives and Differentiability

Explores partial derivatives, differentiability conditions, and verification methods, emphasizing the importance of continuity.

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.