The Einstein field equations are nonlinear and very difficult to solve.

You encode it into equations.

Separable equations.

This tool allows you to solve chemical equations.

This is the calculator, it performs basic chemical calculations.

This is an in con sistent system of equations!

You encode it into equations.

So physicists write equations.

We have three equations with four unknowns.

These two things are parametric equations.

We have fewer equations than unknowns.

And I encourage you to find the equations I already got the slopes for you but find the equations of both of these

They're difficult integrals.

Let's say we have the differential equations and

I have here three linear equations of four unknowns.

Three unknowns with three equations.

Because it's easy to picture the two by two case.

And the equations were written down by James Clerk Maxwell.

But hopefully you might see the parallels if you've already run into exact equations in differential equations.

We have to figure out if they're exact, and if they are exact, we'll use what we know about exact differential equations to figure out their solutions.

And I encourage you to find the equations of both of these

And what we're dealing with are going to be first order equations.

Let's break out our quadratic formula.

And you might remember that slope intercept form were equations of the form, y is equal to mx plus b we did this in the last video where m is the slope, b is the intercept, the y intercept.

So the direction of t's parametric equations is in that direction.

linear equations, x and y.

We're going to start embarking on higher order differential equations.

It's kind of a sub differential equation to solve our broader one.

And I've used it before, when we were just doing linear equations.

I have here three equations of four unknowns.

Eventually, the new model will replace the old model.

Model B is the exact same length as Model A.

Maxwell's equations are of course symmetrical under rotations of all of space.

Let's do some equations of lines in point slope form.

And actually, we're going to start solving non homogeneous differential equations.

See, normally in school, you do things like solve quadratic equations.

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This may make defining the vectors simpler when writing the equations of motion.

This model is directly related to the charity tragedy model.

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