Starting Calc in a few weeks... - Tilted Forum Project Discussion Community

Stompy · 04-12-2004, 12:20 PM

It's the 6 week course, 4 times a week from 7:30 PM - 10 PM (egad, so much math!).

I last had math in the Fall semester of 2002 with Pre-Calc, but I've forgotten a lot of what was covered. Does anyone know off hand the topics that are generally covered in a Calc 1 class?

I'd like to give myself a bit of a head start so I know what to anticipate

Yakk · 04-12-2004, 12:33 PM

What kind of Calc1? Ie, what majors?
Engeneers? Theoretical Mathematicians? English Students? Physics students? Biology majors?

Stompy · 04-12-2004, 12:43 PM

I think this is just your general Calc 1. It's not targetted toward any specific area, really. Basically anyone who needs Calc will take this class.

You get all kinds of students with differing majors. Some will be going into biology while some are going Computer Science.

My major is in Comp. Engineering.

kutulu · 04-12-2004, 12:52 PM

A typical calc class covers limits, derivatives, and integration.

iccky · 04-12-2004, 01:23 PM

Ah calc, how I hate thee.

Like Kutulu said, the biggies are limits, derivatives, and integration. For the most part its memorizing rules and procedures to find these things, which isn't that difficult if you realize what they are measuring.

Limit: Essentially the number a curve approaches as its rate of change gets smaller and smaller.

Derivative: The slope of a tanget line to a curve at a particular point.

Integral: The area under a curve from point a to point b. Also the opposite of a derivative (i.e. if you diferentiate something and then integrate it, you get back what you started with, plus or minus a constant).

If you have any questions just ask here, for some reason its always easier to motivate myself to do other people's homework then my own.

Poloboy · 04-12-2004, 04:46 PM

As for what you need going into the course (i.e. what you may have forgotten from Pre-calc but should probably know), brush up on general trig and algebra. A lot of the content of a first year calculus course is learning to simplify an expression with algebra before using any calculus to analyze it.

WarWagon · 04-12-2004, 05:18 PM

Also, depending on where you go, if they split calc up into two sections, the first will focuse more on differentiation, then they'll bring in integrals and series in the later classes.

Yakk · 04-13-2004, 07:06 AM

Calc1 at my university, from the Calendar:

Quote:

Functions, sequences, limits and continuity. Derivatives and the linear approximation. Applications of the derivative. The Mean Value Theorem and error bounds. Functions of two variables and partial derivatives.

Included was the epsilon-delta definitions of "limit", and the limit definitions of integration and differentiation.

Calc2:

Quote:

Riemann sums and the integral. Antiderivatives and the Fundamental Theorem of Calculus. Applications of the integral. Transforming and evaluating integrals. Improper integrals. Numerical approximation of integrals. Taylor's theorem and polynomial approximation. Convergence of series. Tests for convergence. Functions defined as power series. Taylor series.

However, the university offered 4 or 5 different "calc1" courses, aimed at different kinds of undergrads.

Engeneering Calc1:

Quote:

Functions of engineering importance; review of polynomial, exponential, and logarithmic functions; trigonometric functions and identities. Inverse functions (logarithmic and trigonometric). Limits and continuity. Derivatives, rules of differentiation; derivatives of elementary functions. Applications of the derivative, max-min problems, Mean Value Theorem. Antiderivatives, the Riemann definite integral, Fundamental Theorems. Methods of integration, approximation, applications, improper integrals.

Science Calc1:

Quote:

Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties and inverses. Intuitive discussion of limits and continuity. Introduction to sequences. Definition and interpretation of the derivative, derivatives of elementary functions, derivative rules and applications. Riemann sums and other approximations to the definite integral. Fundamental Theorems and antiderivatives; change of variable. Applications to area, rates, average value.

And then we had:

Quote:

Introductory Calculus For Arts and Social Science
An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models studied will involve polynomial, rational, exponential and logarithmic functions. The major concepts introduced to solve problems are rate of change, optimization, growth and decay, and integration.

Stompy · 04-13-2004, 08:00 AM

Thanks for the replies!

I just downloaded this math program that's geared toward Calc/Statistics which I can use to get a bit of a head start.

I definitely need to reload on some algebra rules/skills. The teachers are actually pretty good about refreshing everyone's memory. I remember back in High School they put the fear into you as if Calc teachers would right off the bat assume you've mastered Algebra (rightfully so, but still.. at that level, people still need a quick referesher)

I knew I shouldn't have waited this long to take the next math

The highest I'll need is Calc 3, and probably one past that.

kutulu · 04-13-2004, 01:50 PM

I don't know if it works this way at all universities, but it did at both that I attended.

If you will be taking calc 1-3, make sure your calc 1 professor uses the same book that most of the calc 2 and 3 professors are using. You don't want to have to buy another book.

supersix2 · 04-13-2004, 01:56 PM

My calc 1 class covered:
Parametric Equations
Vector Fuctions (Dot Product and Cross Product)
Limits
The Derivative
Applications of the Derivative (curve sketching mins/maxs)
Related Rates
Riemann Sums
The Integral

That was my college calc one class. I took calc in highschool my senior year and we covered all that minus vectors and parametric equations but we covered exponentials, natural logs, integral/differentiation of trig fuctions, inverse trig functions.

phukraut · 04-13-2004, 04:35 PM

my calc 1 was split into two semesters and had limits (but not their epsilon/delta proofs; that was left for real analysis 1), the derivative and the integral in the real line of trancendental functions, an introduction into vector calculus (but nothing really beyond Stokes theorem), and convergence of power series and Taylor series. oh yeah, there was also some very rudimentary solving of ODEs.

Stompy · 04-14-2004, 08:35 AM

I wish they'd give a practical application for these methods as they taught them. Perhaps I'd retain a lot of it better if I actually saw HOW it's actually used.

A lot of teachers plop this stuff in front of you and say, "This is a derivative, and this is how you work the problem," but they never actually give you a link to a real world issue of when it would normally be used. It's the age old question of, "When am I actually going to be using this?"

One situation where I heard a lot of this is used is in 3D Graphics programming, which I want to try and get into as I'm going through it all.

Rangsk · 04-14-2004, 01:15 PM

If you want to get a head start, here's a few steps I'd take:

1. Buy the textbook you'll be using.

2. Find the current website for the class you'll be taking, and see if they posted a sylabus and homework problems. For example, I go to UC San Diego, so I'd go to www.ucsd.edu and eventually find this page: http://www.math.ucsd.edu/~gnagy/teac...ter04/Math20A/

3. Follow the sylabus, learning from the textbook and doing the homework problems listed on the website.

4. ???

5. Profit!

Rangsk · 04-14-2004, 01:24 PM

Quote:

Originally posted by Stompy
I wish they'd give a practical application for these methods as they taught them. Perhaps I'd retain a lot of it better if I actually saw HOW it's actually used.

A lot of teachers plop this stuff in front of you and say, "This is a derivative, and this is how you work the problem," but they never actually give you a link to a real world issue of when it would normally be used. It's the age old question of, "When am I actually going to be using this?"

One situation where I heard a lot of this is used is in 3D Graphics programming, which I want to try and get into as I'm going through it all.

Sorry, but this is kind of a rant, and not directed specifically at you. I just need to get it off my chest.

The job of your math professor (unlike, possibly a highschool teacher) is NOT to make you interested in the subject, or tell you exactly why you need to know it. You are taking the course because you signed up for the course, and the professor is going to teach you the course. "If you don't think it's of any use to you, then don't take it," is the generally accepted college course mentality (even if it's a required course). Now, of course, if it is a required course, you can bet your ass that you will need the material for, let's say, all the other courses that it's a prerequisite for! If you can't learn just to learn, then maybe you have a problem with motivation. I find it very childish when people say, "I'm not going to learn this because it has no use to me."

Phew, ok, end of rant

As for when you use calc... well, in pretty much <i>anything</i> with "science" or "engineering" in the title. You won't get far in these courses if you can't do a simple (and many times complex) derivative and integral.

Yakk · 04-14-2004, 01:27 PM

How is calculus used?

Economics without Calculus is playing with crayons. So, if you want to have any clue how the economy works (and, you know, be an educated voter, amoung other useful things), you'll want it. Crayon economics is common (oo, look, pretty graph! It MUST be true!)

Every technical field I know of uses calculus. I guess you could be a technician without knowing it.

Even basic theory of how music works needs forier analysis.

Physics worships calculus. And physics can make you a better pool player. =)

Computer graphics uses linear algebra and calculus up the wazoo.

You could probably make do without calculus in most of those fields. You don't need it to play pool, but it sure helps.

Then again, you could learn how to build a bridge without knowing how to read and write, but god damn would it be harder. =)

supersix2 · 04-14-2004, 01:40 PM

Calculus is awesome. Every day when I go to Calc I am reminded how awesome it is.
I'm really lucky that I have a calc professor who gives us examples of real world calc applications. Also, since my physics is now calculus based I get use it in real world applications there too.

Stompy · 04-14-2004, 02:54 PM

I enjoy the math and I know it'll definitely be needed at some point. I was just saying that I would retain it much better if I had a real world example in which it was actually used.

It's easier to study for a test when you have a better understanding of what exactly it is you're learning, not just how to do it. I remember doing derivatives and logarithms in pre-calc, and in fact I aced those tests. The problem is I was often stuck wondering "What is this actually used for?" I had all the rules memorized and knew how to work the problems, but without any real application, I didn't have a complete understanding of what I was actually doing or what exactly I was working with and what place it held in mathematics.

After people mentioned a few of the things that will be covered, I suddenly remembered some of it from pre-calc.. the stuff I did remember was also given with a real world application. Growth: compounding interest, Decay: radioactive elements, Trig: triangles, sides, angles, etc..

But the few things that didn't stick were the logarithms and derivatives because of a lack of something to attach it to.. a practical use or application.

See what I'm sayin?

[edit]
I guess a good example would be story problems, the kind that give you a real world situation that you could solve by applying the skills you're learning. I recall ones for growth and decay (as mentioned above) being attributed to bank accounts and compounding interest over t time and decaying elements over t time. Trig had a few of those flagpole/shadow problems, but I don't remember any story problems for logarithms or derivatives.

KnifeMissile · 04-14-2004, 03:26 PM

Is being able to isolate the variable x from the equation 2^x = 1024 not good enough for you? You need to see an example of how you might want to isolate a variable in an equation before you can see that it can be useful?

The stories are irrelevant if you can see the utility for yourself. I mean, you can't have seen all possible equations, so do you assume that any equation you haven't seen can't be worth solving? Surely, you agree that this is a silly statement, yet it's pretty much what you are saying...

phukraut · 04-14-2004, 03:59 PM

when i was in highschool taking calculus, a fair bit of our textbook was devoted to deriving the basic equations for velocity and other rates of change. there was also a section on water passing through cones or cylinders. say you have an icecream cone filled with water, and you cut out the bottom, how can you determine the water level after it has dripped out for a certain amount of time. these are simple examples of differential calculus in action.

integrals are all about areas and volumes in the introductory courses.

iccky · 04-14-2004, 04:22 PM

I'm in a statistics course now, and its all extremely complex integrals. Th course is built around getting students ready for the actuarial exam, so thats at least one career path that requires a ton of calc (and actuaries make a lot of money to).

Not the path I'm heading down, because I think it would put me to sleep, but an example.

Essentially to find the probability and likley future occurance of anything, you need to do an integral. So it has application for everything from playing poker to polling to guessing how many people will die of lung cancer in the next 20 years. I'm a political science major and, despite it being a social science many people get into to avoid math, anyone desiring to understand much of the academic literature needs calc.

Stompy · 04-14-2004, 06:50 PM

Now that you mention it, Knife.. yeah, that is pretty handy :P

Man, I really need to review this stuff. Ah well

Thanks for the input!

Rangsk · 04-28-2004, 02:31 AM

I know I went on a rant about not needing this, but I figured it couldn't hurt to let you know.

A VERY common use of logarithms:

Logarithmic scales!

For example:
The Richter scale for earthquakes
The PH scale in chemistry
db scales for sound
Warp Speed (ok, ok, so Star Trek trivia isn't really that useful, but it's fun!)

All of these scales use log base 10. This means that every point is 10 times as large as the previous point. This is because you take the "actual" value and take the log base 10 of it.

So, let's make up a scale where logarithms would be useful- say, how large a living organism is.

We want the smallest organism to be of size 1, but we don't want humans to end up being a huge size... we want something that's down to earth. So, we'll use a base 10 logarithmic scale.

Let's say the smallest creature is the Rhinovirus, which is 2*10^-8 meters. We'll also say a human is about 2 meters. So, now we need to scale these numbers so that the Rhinovirus starts around 1 - we'll use a scale of nanometers. So, that means a Rhinovirus is 20 nanometers, and a human is 2*10^9 nanometers.

Now all we have to do is take the log base 10 of these numbers, and we have an easier to understand scale (we'll call it Rangskians, named after its inventor, me

)

log_10(20) = 1.3 Rangskians
log_10(2*10^9) = 9.3 Rangskians

Now, why is this scale easier to see how large something is? Well, first it will always deal with relatively small numbers. If a virus is around 1 and a human is around 9, then they are numbers that are easy to deal with. Second, you can infer a lot about the numbers. 9.3-1.3 is 8, which means that humans are 10^8 times larger than a virus.

The moral of the story? Logarithms will allow you to take large numbers and reduce them in size drastically.

As for equations that use logarithms, I dare you to solve this equation for y without them:

x^y = 50

(Here's how to solve it)
log(x^y) = 50
ylog(x) = 50
y = 50 / log(x)

You can now graph all possible solutions easily.

As for dervitives, I use them so much, I can't remember how I did math without them. Trust me, you will never regret doing those hundreds of derivitive problems they will make you do in your first calc class.

Yakk · 04-28-2004, 10:30 AM

Yet another example:
Loan Formulas

I can work out how long it will take me to retire, how long it will take to pay off a loan, the effects of increasing my loan/retirement payments, etc.

I didn't know I'd need to know it. Never studied it in school. But, because I knew calculus, I could figure it out. You'd have to pay some smart-ass kid, and trust they knew what they where talking about, and trust your future to their knowledge...

Calculus is like literacy: the ability to read. Some people can't do it, some people can do it well enough to "get by", and others understand it enough to really use it. Being able to read fast/accurately won't help you get a job at the corner store, and you can probably limp on by as even an executive without high end literacy, but god damn it does it help.

04-12-2004, 12:20 PM	#1 (permalink)
Stompy Banned from being Banned Location: Donkey	Starting Calc in a few weeks... It's the 6 week course, 4 times a week from 7:30 PM - 10 PM (egad, so much math!). I last had math in the Fall semester of 2002 with Pre-Calc, but I've forgotten a lot of what was covered. Does anyone know off hand the topics that are generally covered in a Calc 1 class? I'd like to give myself a bit of a head start so I know what to anticipate

04-12-2004, 12:33 PM	#2 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	What kind of Calc1? Ie, what majors? Engeneers? Theoretical Mathematicians? English Students? Physics students? Biology majors? __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

04-12-2004, 12:43 PM	#3 (permalink)
Stompy Banned from being Banned Location: Donkey	I think this is just your general Calc 1. It's not targetted toward any specific area, really. Basically anyone who needs Calc will take this class. You get all kinds of students with differing majors. Some will be going into biology while some are going Computer Science. My major is in Comp. Engineering. __________________ I love lamp.

04-13-2004, 08:00 AM	#9 (permalink)
Stompy Banned from being Banned Location: Donkey	Thanks for the replies! I just downloaded this math program that's geared toward Calc/Statistics which I can use to get a bit of a head start. I definitely need to reload on some algebra rules/skills. The teachers are actually pretty good about refreshing everyone's memory. I remember back in High School they put the fear into you as if Calc teachers would right off the bat assume you've mastered Algebra (rightfully so, but still.. at that level, people still need a quick referesher) I knew I shouldn't have waited this long to take the next math The highest I'll need is Calc 3, and probably one past that. __________________ I love lamp.

04-14-2004, 08:35 AM	#13 (permalink)
Stompy Banned from being Banned Location: Donkey	I wish they'd give a practical application for these methods as they taught them. Perhaps I'd retain a lot of it better if I actually saw HOW it's actually used. A lot of teachers plop this stuff in front of you and say, "This is a derivative, and this is how you work the problem," but they never actually give you a link to a real world issue of when it would normally be used. It's the age old question of, "When am I actually going to be using this?" One situation where I heard a lot of this is used is in 3D Graphics programming, which I want to try and get into as I'm going through it all. __________________ I love lamp.

04-12-2004, 12:52 PM	#4 (permalink)
kutulu Junkie	A typical calc class covers limits, derivatives, and integration.

04-12-2004, 01:23 PM	#5 (permalink)
iccky Psycho Location: Princeton, NJ	Ah calc, how I hate thee. Like Kutulu said, the biggies are limits, derivatives, and integration. For the most part its memorizing rules and procedures to find these things, which isn't that difficult if you realize what they are measuring. Limit: Essentially the number a curve approaches as its rate of change gets smaller and smaller. Derivative: The slope of a tanget line to a curve at a particular point. Integral: The area under a curve from point a to point b. Also the opposite of a derivative (i.e. if you diferentiate something and then integrate it, you get back what you started with, plus or minus a constant). If you have any questions just ask here, for some reason its always easier to motivate myself to do other people's homework then my own.

04-12-2004, 04:46 PM	#6 (permalink)
Poloboy Insane Location: Canada	As for what you need going into the course (i.e. what you may have forgotten from Pre-calc but should probably know), brush up on general trig and algebra. A lot of the content of a first year calculus course is learning to simplify an expression with algebra before using any calculus to analyze it.

04-12-2004, 05:18 PM	#7 (permalink)
WarWagon Loser	Also, depending on where you go, if they split calc up into two sections, the first will focuse more on differentiation, then they'll bring in integrals and series in the later classes.

04-13-2004, 01:50 PM	#10 (permalink)
kutulu Junkie	I don't know if it works this way at all universities, but it did at both that I attended. If you will be taking calc 1-3, make sure your calc 1 professor uses the same book that most of the calc 2 and 3 professors are using. You don't want to have to buy another book.

04-13-2004, 01:56 PM	#11 (permalink)
supersix2 Insane Location: Houston	My calc 1 class covered: Parametric Equations Vector Fuctions (Dot Product and Cross Product) Limits The Derivative Applications of the Derivative (curve sketching mins/maxs) Related Rates Riemann Sums The Integral That was my college calc one class. I took calc in highschool my senior year and we covered all that minus vectors and parametric equations but we covered exponentials, natural logs, integral/differentiation of trig fuctions, inverse trig functions.

04-13-2004, 04:35 PM	#12 (permalink)
phukraut Addict	my calc 1 was split into two semesters and had limits (but not their epsilon/delta proofs; that was left for real analysis 1), the derivative and the integral in the real line of trancendental functions, an introduction into vector calculus (but nothing really beyond Stokes theorem), and convergence of power series and Taylor series. oh yeah, there was also some very rudimentary solving of ODEs.

04-14-2004, 01:15 PM	#14 (permalink)
Rangsk Crazy Location: San Diego, CA	If you want to get a head start, here's a few steps I'd take: 1. Buy the textbook you'll be using. 2. Find the current website for the class you'll be taking, and see if they posted a sylabus and homework problems. For example, I go to UC San Diego, so I'd go to www.ucsd.edu and eventually find this page: http://www.math.ucsd.edu/~gnagy/teac...ter04/Math20A/ 3. Follow the sylabus, learning from the textbook and doing the homework problems listed on the website. 4. ??? 5. Profit! __________________ "Don't believe everything you read on the internet. Except this. Well, including this, I suppose." -- Douglas Adams

04-14-2004, 01:27 PM	#16 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	How is calculus used? Economics without Calculus is playing with crayons. So, if you want to have any clue how the economy works (and, you know, be an educated voter, amoung other useful things), you'll want it. Crayon economics is common (oo, look, pretty graph! It MUST be true!) Every technical field I know of uses calculus. I guess you could be a technician without knowing it. Even basic theory of how music works needs forier analysis. Physics worships calculus. And physics can make you a better pool player. =) Computer graphics uses linear algebra and calculus up the wazoo. You could probably make do without calculus in most of those fields. You don't need it to play pool, but it sure helps. Then again, you could learn how to build a bridge without knowing how to read and write, but god damn would it be harder. =) __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

04-14-2004, 01:40 PM	#17 (permalink)
supersix2 Insane Location: Houston	Calculus is awesome. Every day when I go to Calc I am reminded how awesome it is. I'm really lucky that I have a calc professor who gives us examples of real world calc applications. Also, since my physics is now calculus based I get use it in real world applications there too.

04-14-2004, 02:54 PM	#18 (permalink)
Stompy Banned from being Banned Location: Donkey	I enjoy the math and I know it'll definitely be needed at some point. I was just saying that I would retain it much better if I had a real world example in which it was actually used. It's easier to study for a test when you have a better understanding of what exactly it is you're learning, not just how to do it. I remember doing derivatives and logarithms in pre-calc, and in fact I aced those tests. The problem is I was often stuck wondering "What is this actually used for?" I had all the rules memorized and knew how to work the problems, but without any real application, I didn't have a complete understanding of what I was actually doing or what exactly I was working with and what place it held in mathematics. After people mentioned a few of the things that will be covered, I suddenly remembered some of it from pre-calc.. the stuff I did remember was also given with a real world application. Growth: compounding interest, Decay: radioactive elements, Trig: triangles, sides, angles, etc.. But the few things that didn't stick were the logarithms and derivatives because of a lack of something to attach it to.. a practical use or application. See what I'm sayin? [edit] I guess a good example would be story problems, the kind that give you a real world situation that you could solve by applying the skills you're learning. I recall ones for growth and decay (as mentioned above) being attributed to bank accounts and compounding interest over t time and decaying elements over t time. Trig had a few of those flagpole/shadow problems, but I don't remember any story problems for logarithms or derivatives. __________________ I love lamp. Last edited by Stompy; 04-14-2004 at 03:06 PM..

04-14-2004, 03:26 PM	#19 (permalink)
KnifeMissile Location: Waterloo, Ontario	Is being able to isolate the variable x from the equation 2^x = 1024 not good enough for you? You need to see an example of how you might want to isolate a variable in an equation before you can see that it can be useful? The stories are irrelevant if you can see the utility for yourself. I mean, you can't have seen all possible equations, so do you assume that any equation you haven't seen can't be worth solving? Surely, you agree that this is a silly statement, yet it's pretty much what you are saying...

04-14-2004, 03:59 PM	#20 (permalink)
phukraut Addict	when i was in highschool taking calculus, a fair bit of our textbook was devoted to deriving the basic equations for velocity and other rates of change. there was also a section on water passing through cones or cylinders. say you have an icecream cone filled with water, and you cut out the bottom, how can you determine the water level after it has dripped out for a certain amount of time. these are simple examples of differential calculus in action. integrals are all about areas and volumes in the introductory courses.

04-14-2004, 04:22 PM	#21 (permalink)
iccky Psycho Location: Princeton, NJ	I'm in a statistics course now, and its all extremely complex integrals. Th course is built around getting students ready for the actuarial exam, so thats at least one career path that requires a ton of calc (and actuaries make a lot of money to). Not the path I'm heading down, because I think it would put me to sleep, but an example. Essentially to find the probability and likley future occurance of anything, you need to do an integral. So it has application for everything from playing poker to polling to guessing how many people will die of lung cancer in the next 20 years. I'm a political science major and, despite it being a social science many people get into to avoid math, anyone desiring to understand much of the academic literature needs calc.

04-14-2004, 06:50 PM	#22 (permalink)
Stompy Banned from being Banned Location: Donkey	Now that you mention it, Knife.. yeah, that is pretty handy :P Man, I really need to review this stuff. Ah well Thanks for the input! __________________ I love lamp.

04-28-2004, 02:31 AM	#23 (permalink)
Rangsk Crazy Location: San Diego, CA	I know I went on a rant about not needing this, but I figured it couldn't hurt to let you know. A VERY common use of logarithms: Logarithmic scales! For example: The Richter scale for earthquakes The PH scale in chemistry db scales for sound Warp Speed (ok, ok, so Star Trek trivia isn't really that useful, but it's fun!) All of these scales use log base 10. This means that every point is 10 times as large as the previous point. This is because you take the "actual" value and take the log base 10 of it. So, let's make up a scale where logarithms would be useful- say, how large a living organism is. We want the smallest organism to be of size 1, but we don't want humans to end up being a huge size... we want something that's down to earth. So, we'll use a base 10 logarithmic scale. Let's say the smallest creature is the Rhinovirus, which is 210^-8 meters. We'll also say a human is about 2 meters. So, now we need to scale these numbers so that the Rhinovirus starts around 1 - we'll use a scale of nanometers. So, that means a Rhinovirus is 20 nanometers, and a human is 210^9 nanometers. Now all we have to do is take the log base 10 of these numbers, and we have an easier to understand scale (we'll call it Rangskians, named after its inventor, me ) log_10(20) = 1.3 Rangskians log_10(2*10^9) = 9.3 Rangskians Now, why is this scale easier to see how large something is? Well, first it will always deal with relatively small numbers. If a virus is around 1 and a human is around 9, then they are numbers that are easy to deal with. Second, you can infer a lot about the numbers. 9.3-1.3 is 8, which means that humans are 10^8 times larger than a virus. The moral of the story? Logarithms will allow you to take large numbers and reduce them in size drastically. As for equations that use logarithms, I dare you to solve this equation for y without them: x^y = 50 (Here's how to solve it) log(x^y) = 50 ylog(x) = 50 y = 50 / log(x) You can now graph all possible solutions easily. As for dervitives, I use them so much, I can't remember how I did math without them. Trust me, you will never regret doing those hundreds of derivitive problems they will make you do in your first calc class. __________________ "Don't believe everything you read on the internet. Except this. Well, including this, I suppose." -- Douglas Adams

04-28-2004, 10:30 AM	#24 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	Yet another example: Loan Formulas I can work out how long it will take me to retire, how long it will take to pay off a loan, the effects of increasing my loan/retirement payments, etc. I didn't know I'd need to know it. Never studied it in school. But, because I knew calculus, I could figure it out. You'd have to pay some smart-ass kid, and trust they knew what they where talking about, and trust your future to their knowledge... Calculus is like literacy: the ability to read. Some people can't do it, some people can do it well enough to "get by", and others understand it enough to really use it. Being able to read fast/accurately won't help you get a job at the corner store, and you can probably limp on by as even an executive without high end literacy, but god damn it does it help. __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.