of linear equations.

Partial Differential Equations Index at EqWorld The World of Mathematical Equations.

Partial Differential Equations Methods at EqWorld The World of Mathematical Equations.

have some number of equations, say n equations and n unknowns.

That's true with regular equations or differential equations.

Systems of linear equations.

I was able to reduce this system of equations to this system of equations.

You see above, at the top, a long list of equations with three components for the three directions of space x, y and z.

External links Partial Differential Equations Exact Solutions at EqWorld The World of Mathematical Equations.

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both equations.

Exact equations.

Separable equations.

So both of these parametric equations, both sets of parametric equations have the exact same path.

And this first class of differential equations I'll introduce you to, they're called separable equations.

Math, differential equations.

Two linear equations of to unknowns.

The equations in contexts outside of general relativity are still referred to as the Einstein field equations.

We'll now move from the world of first order differential equations to the world of second order differential equations.

Is the system of linear equations below dependent or independent, and they gave us two equations right here.

Solve the system of equations by graphing.

Solve the system of equations by substitution.

Let's do some examples of solving equations.

Let's solve this set of linear equations.

Let's just solve this system of equations.

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linear equations right here.

So physicists write equations.

Three equations, three unknowns.

So the differential equations.

Partial Differential Equations in Cleve Moler Numerical Computing with MATLAB Example problems with solutions at exampleproblems.com Partial Differential Equations at mathworld.wolfram.com Partial Differential Equations at nag.com Dispersive PDE Wiki NEQwiki, the nonlinear equations encyclopedia

And when you study exact equations in differential equations, you'll see this a lot more.

Anyway, hopefully that these examples made you a little bit more comfortable with graphing equations and reading graphs of equations.

And I just used both of these equations.

We could go to either of these equations.

Now, let's just solve each of these equations.

We'd solve both of these equations for that.

So an equal number of equations and unknowns.

Solve the system of equations using any method.

This is a genuine solution of Einstein's equations.

And I won't prove some of the equations.

I have here three equations of four unknowns.

And in general, one thing that's kind of fun about differential equations, but kind of not as satisfying about differential equations, is it really is just a whole hodgepodge of tools to solve different types of equations.

Two equations and two unknowns.

You encode it into equations.