TELEVISION

Understanding Multivariable Calculus: Problems, Solutions, and Tips

Series: Understanding Multivariable Calculus: Problems, Solutions, and Tips
4.9
(15)
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Episodes
36
Rating
TVPG
Year
2021
Language
English
Publisher
The Great Courses

About

Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards, is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an intellectual exercise for teachers, retired professionals, and anyone else who wants to understand the amazing applications of 3-D calculus.

Related Subjects

Episodes

1 to 3 of 36

1. A Visual Introduction to 3-D Calculus

34m

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Review key concepts from basic calculus, then immediately jump into three dimensions with a brief overview of what you'll be learning. Apply distance and midpoint formulas to three-dimensional objects in your very first of many extrapolations from two-dimensional to multidimensional calculus, and observe some of the new curiosities unique to functions of more than one variable.

2. Functions of Several Variables

30m

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What makes a function "multivariable?" Begin with definitions, and then see how these new functions behave as you apply familiar concepts of minimum and maximum values. Use graphics and other tools to observe their interactions with the xy-plane, and discover how simple functions such as y=x are interpreted differently in three-dimensional space.

3. Limits, Continuity, and Partial Derivatives

30m

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Apply fundamental definitions of calculus to multivariable functions, starting with their limits. See how these limits become complicated as you approach them, no longer just from the left or right, but from any direction and along any path. Use this to derive the definition of a versatile new tool: the partial derivative.

4. Partial Derivatives - One Variable at a Time

30m

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Deep in the realm of partial derivatives, you'll discover the new dimensions of second partial derivatives: differentiate either twice with respect to x or y, or with respect once each to x and y. Consider Laplace's equation to see what makes a function "harmonic."

5. Total Differentials and Chain Rules

31m

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Complete your introduction to partial derivatives as you combine the differential and chain rule from elementary calculus and learn how to generalize them to functions of more than one variable. See how the so-called total differential can be used to approximate ?z over small intervals without calculating the exact values.

6. Extrema of Functions of Two Variables

31m

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The ability to find extreme values for optimization is one of the most powerful consequences of differentiation. Begin by defining the Extreme Value theorem for multivariable functions and use it to identify relative extrema using a "second partials test," which you may recognize as a logical extension of the "second derivative test" used in Calculus I.

Extended Details

  • Closed CaptionsEnglish

Artists

The Great Coursesdirector
The Great Coursesproducer
Bruce H. Edwardsactor