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RubiksCube77
Nov Member 2021

RubiksCube77

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About to do some practice work on node voltage and mesh currents for my circuits class, but as promised I'll do a post on the concept of a derivative.

If we were told to find the slope of let's say f(x) = 4x, we can immediately see the slope is 4. If we didn't know what the function was, but instead got a table of values for a linear function, what could be done to find the slope is rise over run. (y2 - y1)/(x2- x1) is probably something we are all familiar with. Now when we get to a function that isn't linear like x ^2, what will happen if we tried to find the slope of it? We would find out at each different point there isn't a constant slope. If we focus on one specific area, and zoom in fairly close, we would notice that the point is starting to resemble a linear function at that point. Let's say the point is 4. We will use numbers that aren't bigger than 4.5 or smaller than 3.5 to find the slope at 4 using rise over run. By using 4.5, 4.3, and 4.1 we can see that the slope is 8.5, 8.4, and 8.1 respectively. If we use 3.5, 3.7, and 3.9, we get a slope of 7.5, 7.7, and 7.9 respectively. We notice that the value are approaching 8. So we can say that the instantaneous rate of change at 4 is 8 for the function *^2. To take a derivative of a function is to find the instantaneous rate of change at one point of a function.

One might be wondering where would I use such a skill? When I was still taking physics that required calculus, I had to set up a function that modeled a wave, and then I had to find what I believe was the wave's velocity at a position I was given. This was a 3D function, so I had to preform partial derivative to find what I was looking for. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

24-Jul-2015 08:00:58

Adds
Nov Member 2011

Adds

Posts: 9,925 Rune Posts by user Forum Profile RuneMetrics Profile
The speed of dark is the speed of light but there are other types of darkness that can move faster than speed of light. For instance; A shadow.
Across a distance, a shadow can become much larger than the object creating it but still mimic it's source moving in the same way for the same amount of time. So when a shadow is bigger than the object casting it, it moves a greater distance when an object moves but in the same amount of time. Make a shadow large enough and it can travel across the surface faster than light.

Example:

If you here on Earth, cast a shadow on the moon that pointed, say at point A on the moons surface and then you moved your finger so that the shadow moved to point B (The other side of the moon), your finger would only move a few centimetres in a fraction of a second but the shadow it cast on the moon would move thousands of kilometers in the same amount of time. Do it right and you are easily producing a shadow which breaks the light barrier.
Doubt kills more dreams than failure ever will

26-Jul-2015 22:07:01

RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
The concept of integration

Let's just jump straight to the problem. How would we find the area under the curve formed by x^2 from 0 to 1? Some tools I'm sure we all have is how to find the area of basic geometric shapes such as a circle, triangle, square, or rectangle. What one can do to find the area under this curve is by approximating with rectangles. The rectangle's base will all be of equal width delta x, and the height is found by plugging in a point's value in a function. We can say that delta x is 1/3, so we have 3 points 0.33, 0.66, and 1. And for the height of each rectangle we get 0.1089, 0.4356, and 1 respectively. We multiply delta x and height, and get 0.035937, 0.143748, and 0.33. We then add all the values up and we get a rough approximation for what the area is. We then do another set, but this time we make delta x smaller, and we repeat this process until it appears we are approaching a constant value. The constant value is 1/3.

Another thing to add on integration is the fact that we can undo a derivate with an integral and vice versa. For my circuits class, I had to do an integral to find energy since I knew that power = energy over time or as my textbook says dW/dt. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

27-Jul-2015 02:22:40

RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
I might as well show how to do a basic derivative and integral while I'm at it.

To find the general derivative of a function we subtract one from the power and multiply the function by the original power.

Ex. (d/dx) x^2 = 2x

Since we were trying to find what the slope at 4, we evaluate the derivative at 4 and get 8.

For integrals, we reverse what we have to do. We at one to the power of the function and divide by the new power

Ex. (integral) x^2 = (1/3) x^3

If we were trying to find an area under a curve, we would call the integral a definite integral. And we used 0 to 1 in an example so we Evaluate 1 and 0 and subtract the two to get 1/3.

I'll end this by saying that math is important in science and engineering. I'll be taking differential equations and linear algebra next year, so stay tuned for that when I feel like posting on it. Right now I'm going to other threads and then it's off to studying for my circuits class and chemistry class. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

27-Jul-2015 02:31:51

RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
A quote from Bobby Lee on MadTv from the North Korea skit

"I'm a scientist! You're a scientist! Science!" lol

Maybe I didn't pay enough attention to the books, but I found it odd that my physics class didn't go over what would happen if two batteries were hooked up in parallel. I know that two batteries in series can either add or subtract voltage. But what I found from a quick search was that the battery capacity is actually doubled if the two voltages are the same. If they are different, then the battery with the highest voltage discharges into the battery with the lower voltage until both batteries have equal voltages which is apparently a bad thing.

Anyway I want to spend a bit more time with the books, and I have a lab to go do tomorrow. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

31-Jul-2015 08:49:03

RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
Ever wondered if you can turn lead to gold? Well... yes you can thanks to nuclear transmutation. However, it's more efficient to actually mine gold than to make gold using the process. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

01-Aug-2015 04:58:49

Many Much

Many Much

Posts: 4,130 Adamant Posts by user Forum Profile RuneMetrics Profile
Found an interesting things about games.
The
save feature
on early games:
Let's say the Megaman series from NES (if you are familiar with this in your youth).
After each stages, you get a pass word. Yes the pass word is programmed on the game so you can continue from last time by entering the pass word. This is the early save feature.
Newer games started to use batteries to save the games (example Pokemon games).
Later on, flash memories were used with back-up so saved games wouldn't lose save data.
But also newer games still using batteries. Not for saving but to keep the clock-based events to move when not playing. Just an evolution history :P :P :P
How many much more do you want?
:P :P :P

01-Aug-2015 11:29:46 - Last edited on 01-Aug-2015 11:30:02 by Many Much

Goon of Doom

Goon of Doom

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Sorry, but not true ... Darkness is just the absence of light.

Similar o your test of moving your finger and casting the shadow on the moon, imagine putting your hand in a long stream of water coming out of a faucet. Say you block the stream. What happens? No more water flows down (similar to creating a shadow). Then if you observe farther down, that water still falls. It's still traveling, even though it seems that there should be a no-water area (shadow) where your hand went. Same thing with light. Light takes 1.3 seconds to "fall" from earth to moon. Therefore, yes the shadow would be moving quickly across the moon, but not faster than light, because 1. the light would still need to "fall" around the shadow, and 2. Nothing goes faster than light... Not even the absence of light.

06-Aug-2015 19:02:10

B O R A T25

B O R A T25

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Node-voltage

If you have ever taken a course that involved circuits, might you have wondered of one possible way of finding a voltage in a branch without having to use Kirc*hoff's Voltage and Current Laws?

I will quickly go over the concept of node voltage. As usual, this is all done by memory. And if you spot an error, feel free to correct it.

To use Node-Voltage, we need an essential node. An essential node is a point that is connected to three essential branches which are branches that contain elements such as resistors, voltage sources, current sources, etc.

We use the relationship of v/r on each branch and the goal is to find the voltage on each branch.

Here's an example

(v1 - 9)/(r1) + (v1)/(r2) + (v1-v2)/(r2) = 0

is something typical you might see. On the third branch, it's v1-v2 because that branch in this example is connected to another essential node. On the first branch in this example, the branch has a resistor and the resistor is connected to a voltage source.

After setting up equations for all nodes, we use algebra to solve for the voltage.

There's the Mesh-Current method, but that should be for another time. I keep telling people I am Not Sea ! I am African! Appeal to it!
I will abide by the African code of conduct.
I am the real Bad African.

10-Aug-2015 00:08:41

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