YoVDO

APEX Calculus - Functions of Several Variables

Offered By: Sean Fitzpatrick via YouTube

Tags

Calculus Courses Chain Rule Courses Partial Derivatives Courses Matrices Courses Implicit Differentiation Courses Differentiability Courses

Course Description

Overview

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.


Taught by

Sean Fitzpatrick

Related Courses

Calculus: Single Variable
University of Pennsylvania via Coursera
Pre-Calculus
University of California, Irvine via Coursera
Calculus One
Ohio State University via Coursera
Basic Arithmetic
Scottsdale Community College via Canvas Network
Matemáticas y Movimiento
Tecnológico de Monterrey via Coursera