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Establish Equation (7) to finish the proof of the special case of Green's Theorem.

Calculus 3

Chapter 16

Integrals and Vector Fields

Section 4

Green’s Theorem in the Plane

Vector Functions

Johns Hopkins University

Harvey Mudd College

Baylor University

Boston College

Lectures

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

08:32

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

00:02

Complete the proof of the …

03:39

Establish Equation $(10)$ …

09:55

State and prove Green'…

problem. 47. This is equal from seven on. We want to establish it. We can use the same way as we established. You put in sakes. Thanks. So that started with this. This would be a promising to be and acts from Do you want? Why? Do you know why? Right there is. Why? Why? Why? Acts from gets to this and our show and partial acts. E x Do I? So what does that have to stack? I'll use the noodle Abbas. I mean that so and so. And uh X Y c two. Why? Why Finest? Why? What? Why? And you? Why our safety? So what's the next step? Uh, well, here to see what I'm here to see to and I say, where is the C one? You're just the one. Ah, Why? From B to C, Right. So why? From D to Z on. This is everyone. So it is why I need to see. And do you want Why? Why you What? There's a negative. I changed the yeah and thus promise C to d and you are Bye and deter wise, just actually from state to be here from C B. So it has to be Toto. And you are? Uh, yes, right? So just summing. Secretive, Safe. And seventh, we called him five years.

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