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

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

Maxwell developed a set of equations that could unambiguously describe the interrelationship between electric field, magnetic field, electric charge, and electric current.

Older field emission literature (and papers that directly copy equations from old literature) often write some equations using an older equation system that does not use the quantity ε 0.

That's true with regular equations or differential equations.

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both equations.

Exact equations.

Separable 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.

of linear equations.

Math, differential equations.

String cosmology is a relatively new field that tries to apply equations of string theory to solve the questions of early cosmology.

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linear equations right here.

So physicists write equations.

Systems of linear equations.

Three equations, three unknowns.

So the differential equations.

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

I was able to reduce this system of equations to this system of 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 this first class of differential equations I'll introduce you to, they're called separable equations.

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

Two equations and two unknowns.

You encode it into equations.

linear equations, x and y.

least the solvable differential equations.

Two equations with two unknowns.

Three unknowns with three equations.

Let's add the two equations.

So what were linear equations?

That's why they're called 'equations.'

You encode it into equations.

I have separated the equations.

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

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

linear differential equations with constant coefficients.

Two linear equations of to unknowns.

Let's just add these two equations.

Let's do some more nonhomogeneous equations.

And all the equations break down.

So I will rewrite the equations.