MrAl
Flashlight Enthusiast
** Chapters with no discussion found here. **
Hi there :-)
or should i say "good morning!" :-)
I'll try to update my bio sometime today so you can
get an idea who i am and what my education and experiance
has been in the past. If not today, tomorrow for sure.
My smallest power supply design was probably less then
100 milliwatts, and my largest power supply was a 30,000
watt synthesized ac unit using either bipolar or MOSFET
technology over a period of some 20 years.
We're going to start off with some simple stuff just
to get going, then progress into some interesting
circuit analysis. I'll try to keep most of these
short so that it wont take too long to get through.
If this seems elementary it's because it is, and we'll
have to come back to stuff like this later when we look
at complex numbers anyway.
Once we get going i have a feeling it wont be long
before we get into some real deep circuit analysis.
The rewards of course will include understanding our
flashlight circuits better then ever before!
Any errors, suggestions, questions or other matters feel
free to PM me.
Good luck to all of you, especially with your future
circuits!
Serial number: EE-Ch0001-p101
Chapter 1: Math Tools
Like many other crafts, this one requires some tools.
These tools are mostly intellectual ones.
-----------------------------------------------------------
Part 101: Symbols, terms, elementary operations, equations
-----------------------------------------------------------
Symbols
Addition (+)
This simply means that we add one quantity to something else.
Examples:
1+1
3+5
2+9
Notice we can change the order of the operations:
2+9
9+2
and we would get the same answer.
Subtraction (-)
This simply means we subtract one quantity from another.
3-1
5-2
9-1
1-9
Notice here that we cant change the order of the operations.
9-1
is not the same as
1-9
Subtraction is the inverse operation of addition. If we add
3+2
we get '5'
and if we subtract one of the numbers we used for the addition
from the answer '5' we get the remaining number:
5-2 gives us 3, the other number used in the addition, and
5-3 gives us 2.
Terms
Anything separated by an addition sign or a subtraction sign is
called a 'term'.
Examples:
1+3-2
has three terms
3+4+5+6
has four terms
8-3-2+1.33
has four terms
More Symbols
Equals (=)
The equals sign is probably the most important of all. This sometimes
tells us that out of a maybe infinite number of possibilities, only one works.
Examples:
1+1=2
1+2=3
1.4+1.5=2.9
3+5=4+4
Notice that in each case above everything to the 'left' of the
equals sign is equal to everything to the 'right' of it.
This is the way the equals sign works, and it's very useful for
finding answers to some very complex questions.
Not equals (!=) or (<>)
This sign is used to show when something is not equal to something else.
There are two forms in common useage as shown.
4!=5 simply means four is 'not equal' to five.
4<>5 is another way to show this.
Since the symbol "!" is used to show factorial sometimes, it's better
to use '<>' when the context includes calculating factorials.
There is also the equals sign with a question mark, which is used
to show that we have an equation that we dont know is proved to be
true yet.
Example:
4+5?=9
Of course once we prove this, we remove the question mark:
4+5=9
unless of course it proves to be false.
Multiplication (*)
Basic multiplication is just adding the same number over again for
a number of times. Thus, 5*4 means to add 5 four times, or to add
4 five times.
Examples:
1*2
3*7
8*9
9*8
Notice it doesnt matter what order we do the multiplication in,
we get the same answer:
2*3
is the same as
3*2
Division (/)
Division is the inverse operation of multiplication.
Examples:
3/2
5/4
4/2
Notice that the order is important again.
4/2
is not the same as
2/4
Terms and equations
When we have an equation, we simply have a set of terms on
the left and a set of terms on the right.
Examples:
1+2=3+0
4*5+3=3*7+2/1
One important point here is that TERMS are separated by addition
or subtraction signs, NOT by multiplication or division signs.
This last equation
4*5+3=3*7+2/1
thus has only two terms on the left and two on the right.
This is because
4*5
is a single term
and
3*7 and 2/1
are also single terms.
Ok, now here are some self testing questions.
If you cant answer any of these or have problems, just yell!
1. How many terms on the left of: 3+4*2-1=5*2
2. How many terms on the right of: 3+4*2-1=5*2
3. When we multiply 3*2 we get 6. Write at least one way
to show how the inverse operation works.
4. When we add 3+9 and get 12, and then take 12 and
subtract 9 we get 3, which gives us the first number in the
addition back again (3). Why does this happen?
[Later: corrected errors--thanks to Minjin and bindibadgi!]
See ya next time,
Al
Hi there :-)
or should i say "good morning!" :-)
I'll try to update my bio sometime today so you can
get an idea who i am and what my education and experiance
has been in the past. If not today, tomorrow for sure.
My smallest power supply design was probably less then
100 milliwatts, and my largest power supply was a 30,000
watt synthesized ac unit using either bipolar or MOSFET
technology over a period of some 20 years.
We're going to start off with some simple stuff just
to get going, then progress into some interesting
circuit analysis. I'll try to keep most of these
short so that it wont take too long to get through.
If this seems elementary it's because it is, and we'll
have to come back to stuff like this later when we look
at complex numbers anyway.
Once we get going i have a feeling it wont be long
before we get into some real deep circuit analysis.
The rewards of course will include understanding our
flashlight circuits better then ever before!
Any errors, suggestions, questions or other matters feel
free to PM me.
Good luck to all of you, especially with your future
circuits!
Serial number: EE-Ch0001-p101
Chapter 1: Math Tools
Like many other crafts, this one requires some tools.
These tools are mostly intellectual ones.
-----------------------------------------------------------
Part 101: Symbols, terms, elementary operations, equations
-----------------------------------------------------------
Symbols
Addition (+)
This simply means that we add one quantity to something else.
Examples:
1+1
3+5
2+9
Notice we can change the order of the operations:
2+9
9+2
and we would get the same answer.
Subtraction (-)
This simply means we subtract one quantity from another.
3-1
5-2
9-1
1-9
Notice here that we cant change the order of the operations.
9-1
is not the same as
1-9
Subtraction is the inverse operation of addition. If we add
3+2
we get '5'
and if we subtract one of the numbers we used for the addition
from the answer '5' we get the remaining number:
5-2 gives us 3, the other number used in the addition, and
5-3 gives us 2.
Terms
Anything separated by an addition sign or a subtraction sign is
called a 'term'.
Examples:
1+3-2
has three terms
3+4+5+6
has four terms
8-3-2+1.33
has four terms
More Symbols
Equals (=)
The equals sign is probably the most important of all. This sometimes
tells us that out of a maybe infinite number of possibilities, only one works.
Examples:
1+1=2
1+2=3
1.4+1.5=2.9
3+5=4+4
Notice that in each case above everything to the 'left' of the
equals sign is equal to everything to the 'right' of it.
This is the way the equals sign works, and it's very useful for
finding answers to some very complex questions.
Not equals (!=) or (<>)
This sign is used to show when something is not equal to something else.
There are two forms in common useage as shown.
4!=5 simply means four is 'not equal' to five.
4<>5 is another way to show this.
Since the symbol "!" is used to show factorial sometimes, it's better
to use '<>' when the context includes calculating factorials.
There is also the equals sign with a question mark, which is used
to show that we have an equation that we dont know is proved to be
true yet.
Example:
4+5?=9
Of course once we prove this, we remove the question mark:
4+5=9
unless of course it proves to be false.
Multiplication (*)
Basic multiplication is just adding the same number over again for
a number of times. Thus, 5*4 means to add 5 four times, or to add
4 five times.
Examples:
1*2
3*7
8*9
9*8
Notice it doesnt matter what order we do the multiplication in,
we get the same answer:
2*3
is the same as
3*2
Division (/)
Division is the inverse operation of multiplication.
Examples:
3/2
5/4
4/2
Notice that the order is important again.
4/2
is not the same as
2/4
Terms and equations
When we have an equation, we simply have a set of terms on
the left and a set of terms on the right.
Examples:
1+2=3+0
4*5+3=3*7+2/1
One important point here is that TERMS are separated by addition
or subtraction signs, NOT by multiplication or division signs.
This last equation
4*5+3=3*7+2/1
thus has only two terms on the left and two on the right.
This is because
4*5
is a single term
and
3*7 and 2/1
are also single terms.
Ok, now here are some self testing questions.
If you cant answer any of these or have problems, just yell!
1. How many terms on the left of: 3+4*2-1=5*2
2. How many terms on the right of: 3+4*2-1=5*2
3. When we multiply 3*2 we get 6. Write at least one way
to show how the inverse operation works.
4. When we add 3+9 and get 12, and then take 12 and
subtract 9 we get 3, which gives us the first number in the
addition back again (3). Why does this happen?
[Later: corrected errors--thanks to Minjin and bindibadgi!]
See ya next time,
Al
