what is engineering? How do we define,

what is engineering? Well, the definition I like to

use is one put forth by Steve Senturia, one of our professors

who is now retired. He defined engineering to be

the purposeful use of science. All right, so what is 6.002

about? So, 6.002 is a first course in

engineering. And I like to view 6.002 as the

gainful employment of Maxwell's equations.

Many of you have seen Maxwell's equations before.

Most of you should have. And they are hard stuff.

6.002 is all about teaching you how to simplify our lives,

make things simple. So, if you can gainfully employ

Maxwell's equations, gainfully employ the facts of

nature to build very interesting systems.

So let me show you how the transition is made.

So, there's a world around us, nature, so we made some

observations in nature. We make measurements,

and we can write down large tables of measurements.

So, for example, we can take objects and measure

the voltage across them, and look at the resulting

current through the elements. So, we may end up getting a

bunch of values such as [CHALKBOARD].

So, we start out life with making measurements on what

exists. And we build a bunch of tables.

Now, we could directly take these tables,

and based on observations of these tables,

we could go ahead and build very interesting engineering

systems that help us out in day-to-day lives.

But that's incredibly hard. Imagine having to resort to a

set of tables to do any kind of useful work.

So what we do as engineers, we first layer a level of

abstraction. We look at all the data,

and somehow layer abstraction such that we can simplify or

much more succinctly put in a simple equation or a simple

statement what these numbers are telling us.

OK, so for example, our physics laws,

so laws of physics for example are simply abstractions,

the laws of abstractions. So, these sets of numbers can

be codified by Ohm's law, for example,

V is equal to RI, the voltage current,

relates to the resistance of the object.

So, V is equal to RI is a law that succinctly describes a set

of experiments, and replaces a large number of

tables with a very simple statement.

You could call this the law, or you could call it an

abstraction. OK so you see laws of physics,

call them abstractions of physics if you like.

Similarly, there are Maxwell's equations and so on and so

forth. So, this is what is.

This is what's out there. OK, and a law as an abstraction

describe the properties of nature, as we see it,

in some succinct form. Now, if you want to go and

build useful things, we could take these

abstractions, take Maxwell's equations,

and go and build things. But it's hard.

It's really, really hard.

And what you learn in, at MIT is this place is all

about simplifying things. Take complicated things,

build layers of abstraction, and simplify things so that we

can build useful systems. Even in 6.002 we start life by

making a huge leap from Maxwell's equations to a couple

of very, very simple laws. OK, I'm going to show you that

leap that we will make today. So, the first abstraction that

we layer is called the lump circuit abstraction.

OK, in the lump circuit abstraction, what we do is we

make a set of simplifications that allows us to view a set of

objects as discrete or lumped elements.

So, we may, I will define voltage sources.

We'll define resistors. We'll define capacitors,

and so on. OK, and I'm going to make the

jump, and show you how we make the jump in a few minutes.

So, on that sort of abstraction, we then layer yet

another abstract layer. And let me call that the

amplifier abstraction. OK, remember,

here we are absolutely down and dirty.

We are setting the probes, measuring objects,

and building huge tables. We abstracted things into

simple laws, and life got a little better.

OK, I'm going to show you can abstract things further out and

build discrete objects, and, you could build even more

interesting components called amplifiers and begin playing

around with amplifiers. OK, so when you are using

amplifiers, you don't really have to worry about the details

of Maxwell's equations. OK, I'll give you some very

simple abstract rules of behavior for an amplifier,

and you can go build very interesting systems without

really, really knowing how Maxwell's equations applies to

that because you will be working at this abstract layer.

However, since you're engineers, and you are good at

building such systems, it's very important for you to

understand how we make this leap from the laws of physics into

some of our very primitive engineering abstractions.

So, once we make the amplified abstraction in 6.002,

by the way, 6.002 starts here. We start from the laws of

physics and then proceed all the way out.

So, once we talk about amplifiers we will take two

pads. On the amplifier,

you will build the next abstraction called the digital

abstraction. OK, and with the digital

abstraction, we will build new elements such as inverters and

combinational gates, OK?

So, notice we are building bigger, and bigger things,

which have more and more complicated behavior inside

them, but which are very simple to describe, right?

So, following the digital abstraction, we will superimpose

the combinational logic abstraction on top of that,

and define functional blocks that look like this:

some inputs, some function,

some outputs. The next abstraction on top of

that will be the clock digital abstraction, where we will have

some notion of time introduced into the system.

There will be a clock, and this will be some function.

And there will be a clock that introduces time into the sort of

logic values that functions operate upon.

Following that, the next level of abstraction

that we build is called instruction set abstraction.

OK, now you begin to see things that consumers get to look at.

Can someone give me an example of, or name an instruction set,

or instruction set abstraction? Bingo.

So, x86 is one set of abstractions.

And in fact, in many universities,

education could well start just by saying, OK,

here's an abstraction. These are the x86 instructions,

OK? Some MIT gurus have designed

this awesome little microprocessor,

OK? So you just worry about,

you take this abstraction layer here, the assembly instructions,

and you go and build systems on top of that.

OK, so this is an abstraction layer called the x86 layer.

There are other abstraction layers.

In 6.004, you will learn about, I believe, the alpha or the

beta, OK, and various other abstractions at this point.

So, 6.002 kind of goes until here.

6.002 takes me from the world of physics all the way to the

world of interesting analog and digital systems.

OK, 004, the course on computation structures,

will show you how to build computers all the way from

simple digital objects all the way to big systems.

Following that, you learn about language

abstractions, Java, C, and other languages,

and that's in 6.002. And there are several other

courses that will cover that. Following this,

you learn about software system abstractions,

and software systems, you will learn about operating

systems. Any example of an operating

system abstraction that people know out there?

What's that? Linux.

What else? I'm just wondering how long

I'll have to go before I hear what I want to hear.

[LAUGHTER] OK, so we have a bunch of software

systems. So, if we have a bunch of

software systems, these are nothing but

abstractions. Linux simply implies a set of

system calls that the programs must adhere to.

Windows is another set of system calls.

That's it. And see how much money they

made out of it? OK, it's all about abstraction

layers, that all start from nature.

All right? Build abstraction upon

abstraction upon abstraction upon abstraction,

and someone out here are lots of dollars.

OK, so based on these abstractions,

we can then build useful things for human beings.

We can build very useful things, video games,

so we can send space shuttles up, and a whole bunch of other

systems. But it's based on these

abstraction layers. What's unique about education

at MIT? What's unique about 6.002 and

EECS? Is to my knowledge,

there are not many other places in the world where you will get

an education in everything going all the way from nature to how

to build very complicated analog and digital systems.

OK, we will show you layer upon layer upon layer upon layer,

peel away the onion until you are down to raw nature,

OK, through Maxwell's equations.

So, 6.002, 004, this is 033,

OK, 6.170, and so on. OK, the whole EECS is about

building abstraction layers, one on top of the other.

So that's one path. There's the analog path.

The analog path would take an amplifier, and build an

abstraction layer called the op-amp.

See how similar they all look? You know the amplifier,

the inverter of the digital world, and the operational

amplifier in the analog world, just different ways of looking

at the same devices. So, to build an analog system,

to build an operational amplifier, and then,

here we go end up building a whole bunch of different

interesting analog system components.

OK, and these components might look like oscillators.

They might look like filters. OK, they look like power

supplies, a whole bunch of very interesting abstract components,

which pulled together can then give you the next set of

systems. And these systems might be

toasters, or say for example other analog systems like the

various control systems for various power plants and so on

and so forth, and ultimately,

fun and dollars. OK, so 6.002 is about going

from physics all the way to this point.

We will build interesting analog systems,

and take you up to interesting digital system components,

from which 004 will take you all the way to building computer

architectures. So that, in a nutshell,

kind of gives you a feel for the space of EECS.

OK, this chart here is almost a vignette of what EECS at MIT is

all about. And this is the world according

to Agarwal, because he's teaching 002.

OK, so this is 6.002, and the rest of EECS is

somewhere out there. OK, so I'm going to do now is

throughout this course; I want you to think about which

part in this vignette we are in. So, right now,

I'm going to start here and take you here.

OK, and as you get closer and closer, things get simpler,

and simpler, and simpler.

Still, the final abstractions are pedal, brake,

steering wheel. I mean, that's the abstraction

to play a game, right, four or five very simple

interfaces, and that's all you need to know.

And everybody in the world can play stuff.

So remember, this stuff is complicated.

This stuff is very, very simple.

OK, and the more we build abstractions and come to this

side, things get simpler and simpler.

So, a large part of what I'll cover today is make the biggest

simplification. The biggest simplification we

will make his go from Maxwell's equation to some very,

very simple algebraic rules. OK, I did Maxwell's equations

myself. And I tell you,

they were very interesting stuff but complicated.

I can't imagine building efficient systems using

Maxwell's equations. So, let's take an example,

OK? So, let's say I have a battery.

Just switch to page three of your course notes.

And let's say I connect that to a bulb.

OK, and this is a wire. And, the battery supplies some