Name: Understanding Multivariable Calculus: Problems, Solutions, and Tips
Released: 2014-05-09T00:00:00.000Z
Cast: Bruce H. Edwards

TV Show · Educational · Documentary

The next step for students and professionals to expand their knowledge for work or study in quantitative fields; an intellectual exercise for teachers, retired professionals and anyone else who wants to understand the applications of 3-D calculus.

2014 · 33m

Starring Bruce H. Edwards

EPISODE 1

A Visual Introduction to 3-D Calculus

Reviewing key concepts from basic calculus; a brief overview of what is to be learned; applying distance and midpoint formulas to three-dimensional objects; observing some of the new curiosities unique to functions of more than one variable.

33m
EPISODE 2

Functions of Several Variables

What makes a function "multivariable"; beginning with definitions; how these new functions behave as one applies familiar concepts of minimum and maximum values; using graphics and other tools to observe their interactions with the xy-plane.

30m
EPISODE 3

Limits, Continuity, and Partial Derivatives

Applying fundamental definitions of calculus to multivariable functions, starting with their limits; how these limits become complicated as one approaches them; using this to derive the definition of a versatile new tool, the partial derivative.

30m
EPISODE 4

Partial Derivatives - One Variable at a Time

Discovering the new dimensions of second partial derivatives; differentiating either twice with respect to x or y, or with respect once each to x and y; considering Laplace's equation to see what makes a function "harmonic".

30m
EPISODE 5

Total Differentials and Chain Rules

Combining the differential and chain rule from elementary calculus; how to generalize them to functions of more than one variable; how the total differential can be used to approximate ?z over small intervals without calculating the exact values.

31m
EPISODE 6

Extrema of Functions of Two Variables

The ability to find extreme values for optimization is one of the most powerful consequences of differentiation; defining the Extreme Value theorem for multivariable functions; using it to identify relative extrema using a "second partials test".

30m

Bruce H. Edwards

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Season 1

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