You can toss them into the same set of equations.

We first captured the dynamics with a set of differential equations.

Every thousand feet above, is a whole new set of equations

We've just abstracted what the retina's doing with a set of equations.

looked at a whole set of symmetries of Maxwell's equations, which are called special relativity.

So what it's doing is, it's replacing the retinal circuitry, really the guts of the retinal circuitry, with a set of equations, a set of equations that we can implement on a chip.

There's a set of linear algebra equations that implement the Kalman filter and higher dimensions.

That's one of our equations.

Exact equations.

Separable equations.

That's true with regular equations or differential equations.

It satisfies both of these equations.

Two linear equations of to unknowns.

solve the systems of linear equations by graphing. and they give us two equations here.

When we say system of equations, we just mean many equations that have many unknowns.

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

The density of matter is finite, and we have a chance of a consistent set of equations that can describe the whole process.

Ben's current age and then maybe we could set up some equations and solve for this.

These mathematical equations are concise notations for a possibly large set of values, especially if I do something like this.

Math, differential equations.

No? Nonlinear equations?

Let's do some examples of solving equations.

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

Determine the number of solutions for each of these equations, and they give us three equations right over here.

And that's a fairly useful thing, because differential equations is something that shows up in a whole set of different fields.

An Assistant dialog to simplify solving 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.

So it's a system of two linear equations.

An image comes in, goes through the set of equations, and out comes streams of electrical pulses, just like a normal retina would produce.

Solve Chemical Equations Viewer

Add the two equations.

linear equations right here.

Equations. The universal language.

So the differential equations.

05 is very tempting, but regular expressions are string equations, not mathematical equations.

So this is the whole point of exact equations.

And then we just solve both of these equations.

Welcome to the presentation on systems of linear equations.

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.

Generate images from LaTeX equations

Two equations and two unknowns.

Differential equations are something different.

Here are our equations again.