🟡01 - Functions of Several Variables (Domain and Range of a function)

In this lesson we are going to start a new course - Multivariable Calculus or Calculus 3

Functions of Several Variables: are functions that take multiple inputs (more than one input) to produce a single output or multiple outputs.

We shall in this lesson expose ourselves to functions of two or more variables and how to find the range and domain of such functions.

A function of two variables x and y may be presented in the form, z = f(x,y). And example is a function of two variables is the area of a rectangle, thus
A = l * w, then: A = f(l,w) = l * w

A function of three variables x, y and z may as well be presented in the form, w = f(x,y,z). And example is a function of three variables is the volume of a rectangular box, thus
V = l * w * h, then: V = f(l,w,h) = l * w * h

Domain: the set of ordered input values that produce a unique real value for the independent variable OR the set of ordered input values that makes the function defined.

Range: the set of output values of the function.

Playlists on various Course
1. Applied Electricity

2. Linear Algebra / Math 151

3. Basic Mechanics

4. Calculus with Analysis / Calculus 1 / Math 152

5. Differential Equations / Math 251

6. Electric Circuit Theory / Circuit Design

7. Calculus with Several Variables

Make sure to watch till the end.
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Thank you.

[SkanCityAcademy_SirJohn]

9:00 - 10:32 The range of eg 1, ie. z = x^2 + y^2, is Z = [0, +inf) or z >=0 since any set of (x, y) will make z either 0 or a positive real number. Kindly take note.

[ApochieIshmael]

Wow! indeed you are doing marvelous well in your delivery

[nahomtesfaye]

you're good teacher thank you a lot

[mathsetc.]

Nice informative video. One correction suggested. The range of z=x^2+y^2 is [0, Infinity) because of the squares and not the interval as shown in the video.

[DanielOluwafemi-xdjy]

You are certainly Ghanaian! 😂
Enjoying you from Nigeria though!

[EdisonvsTesla]

ln(y-2x)≥0=y-2x ≥1
. And y-2x>0 . I think it has two solution, we can take their intersection, thanks in advance from Ethiopia 🇪🇹

[nimtohs]

Please try to make short videos too please… for quick understanding for test

[mhlengincama]

in 18:03 is'nt the range (-inf to 0)u(0 to 1) because 1 over something will always bring value less than 1?

[RRR_ACADEMY]

Thank you Sir! I am from Sri Lanka! I am also conducting Educational youtube channel Sir☺

[lesediphora]

please introduce Limits and Continuity

[longolongogoodson]

We want videos on ac circuits also Sir