APEX Calculus - Functions of Several Variables

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.

Syllabus

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.