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Notation for functions of several variables

Limits and continuity

Defining partial derivatives

Interpreting partial derivatives

Partial derivatives

Second-order partials and differentiability classes

Differentiability in two variables

Showing that a function is differentiable

Differentiability in general

Chain rule

Chain rule examples

Chain rule with matrices

Implicit differentiation

Directional derivatives: definition

Directional derivatives: examples

Directional derivatives: interpretation and significance

Extreme values and critical points

Finding critical points

Classifying critical points

Classifying critical points: Example #1

Classifying critical points: Example #2

Finding extreme values: Example #1

Finding extreme values: Example #2

Introducing Lagrange multipliers

Lagrange multipliers: Example #1

Lagrange multipliers: Example #2

Description:

Explore functions of several variables in this comprehensive video series for Calculus IV. Delve into topics like limits, continuity, partial derivatives, differentiability, chain rule, implicit differentiation, directional derivatives, extreme values, critical points, and Lagrange multipliers. Learn notation, interpret concepts, and work through numerous examples to master multivariable calculus. Gain additional insights beyond the standard APEX Calculus textbook content, enhancing your understanding of advanced mathematical concepts.

APEX Calculus - Functions of Several Variables

Sean Fitzpatrick

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#Mathematics #Calculus #Chain Rule #Partial Derivatives #Algebra #Linear Algebra #Matrices #Implicit Differentiation #Differentiability

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