Multivariable Calculus: Introduction to functions of multiple variables

Описание: In this lecture we look at scalar-valued functions of multiple variables, e.g. z=f(x,y) and w=f(x,y,z), focusing on their notation, domain, range, and graphical representation. We explore functions mapping from ℝ^2 and ℝ^3 to ℝ, understanding how these functions translate into geometric shapes in higher dimensions.

Multivariable Calculus Unit 3 Lecture 1

Key Points
Real-valued functions map vectors to scalars, contrasting with the vector-valued functions we studied previously (which mapped scalars to vectors).
The graph of a continuous function from ℝ^2 to ℝ is a surface in ℝ^3.
Functions from ℝ^3 to ℝ cannot be graphed as the image would be in four-dimensional space.

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