This course on Functions of Several Variables aims to teach students the notation, limits, continuity, and partial derivatives of functions with multiple variables. By the end of the course, students will be able to interpret and find partial derivatives, understand differentiability in two variables, apply the chain rule, work with matrices, and utilize implicit differentiation. The teaching method includes theoretical explanations, examples, and problem-solving sessions. This course is intended for students studying advanced calculus or mathematics at the university level.
APEX Calculus - Functions of Several Variables
Overview
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
