Fundamentally, calculus is split into two parts. Pre-calculus is meant to teach you how to manipulate numbers and functions. The first of calculus teaches you to understand how numbers and functions change i.e. rate, derivative, dy/dx.
For example, the function f(x)=x is a linear function that goes from one corner to the opposite (in a Cartesian plane). Calculus skills show you that the rate that the y coordinate changes with respect to the x coordinate is 1 e.g. (0,0),(1,1),(2,2). You'll learn rules that tell you that the derivative of the function f(x)=x is 1 and that the derivative of f(x)=ln(x^2) is 2/x. This is what the derivative is- a rate of change.
Once you master this half of calculus, you'll learn how to do the opposite. Instead of derivation you'll deal with integration, going backwards. The integral of 3x^2 is x^3, the integral of e^x is e^x. It looks confusing now but once you understand the logic and rules it'll clear up. If you are not taking the AP track then you don't have to worry about integration.
Good luck.
For example, the function f(x)=x is a linear function that goes from one corner to the opposite (in a Cartesian plane). Calculus skills show you that the rate that the y coordinate changes with respect to the x coordinate is 1 e.g. (0,0),(1,1),(2,2). You'll learn rules that tell you that the derivative of the function f(x)=x is 1 and that the derivative of f(x)=ln(x^2) is 2/x. This is what the derivative is- a rate of change.
Once you master this half of calculus, you'll learn how to do the opposite. Instead of derivation you'll deal with integration, going backwards. The integral of 3x^2 is x^3, the integral of e^x is e^x. It looks confusing now but once you understand the logic and rules it'll clear up. If you are not taking the AP track then you don't have to worry about integration.
Good luck.
So
Lifer
- Jul 2, 2001
- 25,923
- 17
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Add an extra lol there for good measure.
Math doesn't come easy for everyone, and some professors are just terrible at explaining things.
Math is like anything else in life, it's a skill that requires practice. Some people have more raw talent at it than others, but raw talent is not skill. I was in one level above retard math in middle school at one point and I worked my ass off to "get it". I graduated college with a math minor and now people think I'm a genius at math (I'm not). It requires work, perseverance, and a good teacher or two along the way.
It seems a lot of people sit down and expect to be great at math with no practice whatsoever. They quit on the first try and declare themselves "no good at math."
People don't expect to be the next Neil Pert or the next Barry Bonds by just showing up and trying. Why do they think math is different? Yes it can be boring, but so can music practice all day every day, and I'd imagine that standing in a batting cage eight hours a day every day for years gets old eventually.
Fenixgoon
Lifer
- Jun 30, 2003
- 33,140
- 12,560
- 136
so is functional calc the generalized and broadened version of fourier/laplace's series expansions?
guyver01
Lifer
- Sep 25, 2000
- 22,135
- 5
- 61
EarthwormJim
Diamond Member
- Oct 15, 2003
- 3,239
- 0
- 76
Calculus is basically about finding the area under the curve of a line (integral), or finding the derivative (slope) of a line at some point tangent to it or generalized.
I'm sure you know how to find the slope of a straight line, well with calculus you can actually prove the method of how you found that slope, and do it for more complex equations (not of the form y=mx+b)
Pre-Calculus is just more Algebra to get you ready for Calculus. When you're in Calculus, algebra should be so ingrained into your head that it's as easy as doing addition/subtraction etc.
You might at the end start getting into the fundamental theorem of calculus though (my class did in high school).
A nice example of how it is used is distance vs time, velocity, acceleration and jerk.
Imagine that the distance of some object is plotted over time.
Velocity is the derivative (read: slope) of distance vs. time.
Acceleration is the derivative of velocity.
Jerk is the derivative of acceleration.
Conversely the opposite is true using integration.
Acceleration is the integral of jerk etc...
I'm sure you know how to find the slope of a straight line, well with calculus you can actually prove the method of how you found that slope, and do it for more complex equations (not of the form y=mx+b)
Pre-Calculus is just more Algebra to get you ready for Calculus. When you're in Calculus, algebra should be so ingrained into your head that it's as easy as doing addition/subtraction etc.
You might at the end start getting into the fundamental theorem of calculus though (my class did in high school).
A nice example of how it is used is distance vs time, velocity, acceleration and jerk.
Imagine that the distance of some object is plotted over time.
Velocity is the derivative (read: slope) of distance vs. time.
Acceleration is the derivative of velocity.
Jerk is the derivative of acceleration.
Conversely the opposite is true using integration.
Acceleration is the integral of jerk etc...
Last edited:
destrekor
Lifer
- Nov 18, 2005
- 28,799
- 359
- 126
If you understand algebraic equations, pre-calc won't be too difficult, barring the fact you don't have a terrible class.
Remember this is a course, you didn't sign up to only take the final and receive no instruction prior to said final. The course, like all math courses, will be filled with material of gradually-increasing difficulty as the weeks pass, it's not like the hardest calculus equations are going to be shoved down your throat on day one.
In short: pre-calc is a good class to see if you are capable of very-basic calculus. From there, you can see if you are going to need a lot of help passing the first calculus course.
Remember this is a course, you didn't sign up to only take the final and receive no instruction prior to said final. The course, like all math courses, will be filled with material of gradually-increasing difficulty as the weeks pass, it's not like the hardest calculus equations are going to be shoved down your throat on day one.
In short: pre-calc is a good class to see if you are capable of very-basic calculus. From there, you can see if you are going to need a lot of help passing the first calculus course.
destrekor
Lifer
- Nov 18, 2005
- 28,799
- 359
- 126
yeah, my high school Pre-Calc class was basically more advanced algebra (compared to the high school algebra 2), throw in some advanced geometry objectives, and get acquainted with the uses and purpose of calculus and dab a little into what you can do in calc.
Of course, calculus is an extremely convoluted mathematical discipline filled with an insane number of WTFs, so in pre-calc you aren't really going there, more or less you are looking toward the Horizon of WTF, and at the end of the instruction you receive a candle for your journey toward the WTF Abyss and a vague idea of exactly WTF all this WTF is actually about.
I despise calculus, in case anyone is wondering. ^_^
- Dec 11, 1999
- 16,648
- 4,589
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Calculus is taught in three parts. The first thing they'll try to teach you is limits. The only reason they try to teach you limits is so that they can prove that differentiation (see below) works. This is pretty much pointless. You know about the quadratic formula and completing the square for solving quadratic equations, right? Do you care how they work? Most of the time I just use them. So just remember enough of limits to get you through the tests on them, and forget the rest.
Next is differential calculus, which is a method for finding the derivative of a function. (See quote above.) It produces another function whose value is the slope of the original function at any given point. Differential calculus is kind of similar to completing the square, and a lot like baking a cake. Follow the rules and it will turn out fine.
Finally (as far as basic calculus goes) comes integral calculus. Integrating a function is the process of finding what function you'd need to take the derivative of to get the function you're working with. If a derivative is baking a cake, an integral is reverse-engineering a cake (figuring out how much of which ingredients went into it.) As you might imagine, this process is difficult, not always possible without dragging a computer into it, and always leaves a margin for error. One or more undefined constants are usually part of the answer; though these constants may become defined when the integral is applied to a word problem.
So to summarize, limits are stupid, derivatives are cool, and integrals are messy. ^_^
Fournier.... transform?
AHHHHHHHHHHHHHHHHHHHHHH
<runs screaming from room>
This is why I didn't finish my minor in physics. :ninja: (That big S is the symbol for an integral.)
fatpat268
Diamond Member
- Jan 14, 2006
- 5,853
- 0
- 71
Calculus is taught in three parts. The first thing they'll try to teach you is limits. The only reason they try to teach you limits is so that they can prove that differentiation (see below) works. This is pretty much pointless. You know about the quadratic formula and completing the square for solving quadratic equations, right? Do you care how they work? Most of the time I just use them. So just remember enough of limits to get you through the tests on them, and forget the rest.
Eh, I wouldn't go that far. Luckily, limits are an easy concept (although the episilon delta definition isn't
) to learn, and will help your understanding later on.Your success in calculus really depends on how well you understand the source material and there isn't some magical formula most of the time.
DrPizza
Administrator Elite Member Goat Whisperer
Calculus.
The teacher makes a huge difference in how easy the course will be for you. If you don't understand the way the teacher explains it, find someone or something (book, endless youtube videos) that DO explain it so that you can understand it. You can always feel free to ask someone here to explain a concept or two; generally you'll get a decent balance of idiots/trolls/nefs to actual good help.
By far, the MOST important part of taking calculus: practice, practice, practice. There are some concepts in calculus that are incredibly simple to explain, but that take a shitload of practice to master. For example, the chain rule. I can teach that rule, explain that rule, and show how it's derived (cause I never pull rules from thin air) and I can give 3 or 4 solid examples in under 10 minutes. And, then I'm done for that day. But (since I teach 5 days a week) I give homework problems on it for 3 consecutive nights to make sure everyone has mastered it. Some master it within 15 practice problems, others take 50 or more before they can apply that rule without errors. Once you've mastered that rule, an additional 25 problems takes you 10 minutes, so no real harm in loading up the homework. But seriously, I can't count how many people say "but it seemed so easy in class" after bombing a test because they didn't practice it.
So, according to schneiderguy, f(x)=e^x. So, f'(x)=xe^(x-1)?? FAIL! I don't think the OP should have to pay for errors. Or does schneiderguy mean when the exponent is a real number? f(x)=pi^4
According to schneiderguy, the derivative would be 4pi^3. Wrong again.
Anyway, OP, calculus as someone said above is like a new toolbox for dealing with real world problems. (Tis a shame that most texts/profs don't give enough time to real world examples.) The first half of calculus deals with instantaneous rates of change. Do things in the real world change? Of course. At what rate? Well, if you graph it and the graph is a straight line, then you've probably learned long ago that y=mx+b, the rate of change is the slope which is the value m. But, if it's a non-linear relationship, then to find the rate of change (which varies), then you need calculus.
Where are you? That's your position. If your position is changing, we call the rate that your position changes your speed. Or, more appropriately, your velocity (which will take into account whether you're moving forward or backward.) If your speed isn't constant, the rate of change of speed is called your acceleration. ("Deceleration" is generally treated as a negative acceleration.) There are a lot of applications in physics, but there are also a lot of other areas where calculus can be applied, such as business, biology, (heck, probably any science), etc.
The teacher makes a huge difference in how easy the course will be for you. If you don't understand the way the teacher explains it, find someone or something (book, endless youtube videos) that DO explain it so that you can understand it. You can always feel free to ask someone here to explain a concept or two; generally you'll get a decent balance of idiots/trolls/nefs to actual good help.
By far, the MOST important part of taking calculus: practice, practice, practice. There are some concepts in calculus that are incredibly simple to explain, but that take a shitload of practice to master. For example, the chain rule. I can teach that rule, explain that rule, and show how it's derived (cause I never pull rules from thin air) and I can give 3 or 4 solid examples in under 10 minutes. And, then I'm done for that day. But (since I teach 5 days a week) I give homework problems on it for 3 consecutive nights to make sure everyone has mastered it. Some master it within 15 practice problems, others take 50 or more before they can apply that rule without errors. Once you've mastered that rule, an additional 25 problems takes you 10 minutes, so no real harm in loading up the homework. But seriously, I can't count how many people say "but it seemed so easy in class" after bombing a test because they didn't practice it.
So, according to schneiderguy, f(x)=e^x. So, f'(x)=xe^(x-1)?? FAIL! I don't think the OP should have to pay for errors. Or does schneiderguy mean when the exponent is a real number? f(x)=pi^4
According to schneiderguy, the derivative would be 4pi^3. Wrong again.
Anyway, OP, calculus as someone said above is like a new toolbox for dealing with real world problems. (Tis a shame that most texts/profs don't give enough time to real world examples.) The first half of calculus deals with instantaneous rates of change. Do things in the real world change? Of course. At what rate? Well, if you graph it and the graph is a straight line, then you've probably learned long ago that y=mx+b, the rate of change is the slope which is the value m. But, if it's a non-linear relationship, then to find the rate of change (which varies), then you need calculus.
Where are you? That's your position. If your position is changing, we call the rate that your position changes your speed. Or, more appropriately, your velocity (which will take into account whether you're moving forward or backward.) If your speed isn't constant, the rate of change of speed is called your acceleration. ("Deceleration" is generally treated as a negative acceleration.) There are a lot of applications in physics, but there are also a lot of other areas where calculus can be applied, such as business, biology, (heck, probably any science), etc.
TecHNooB
Diamond Member
- Sep 10, 2005
- 7,458
- 1
- 76
Fournier.... transform?
AHHHHHHHHHHHHHHHHHHHHHH
<runs screaming from room>
fourier analysis is a beautiful thing!
Fournier.... transform?
<3 the stuff of my dreams
i dont really get it either, that stuff can be challenging, but i dont see how it was anymore challenging than learning calc for the first time around. although i do admit i got lucky and had a kickass teacher when i first learned the stuff.
EarthwormJim
Diamond Member
- Oct 15, 2003
- 3,239
- 0
- 76
It makes life so much easier with signal processing for EE though (bleck at time domain). Plus once you get past the proof part, you can often manipulate things so you can do table look up.
Precalc was pointless. Just a rehash of Alg II/Trig for us, with just a tad bit extra time spent on polars and parametrics.
Ms. DICKINSON
Golden Member
yhelothar
Lifer
- Dec 11, 2002
- 18,409
- 39
- 91
The fundamental principles of calculus is simple. Calculus is all about the math of rate of change. That's what derivative is. You've done derivatives before in algebra, it's just finding m or slope of the equation/line.
Although derivatives in algebra is very simple as it only involves linear functions. Slope is a fixed number and is always constant.
But how do you find the rate of change of a curve? This is what calculus and derivatives is all about.
Khan aside, this guy is also really good.
http://www.youtube.com/watch?v=EX_is9LzFSY&p=C9298085590E88D5&playnext=1&index=15
Although derivatives in algebra is very simple as it only involves linear functions. Slope is a fixed number and is always constant.
But how do you find the rate of change of a curve? This is what calculus and derivatives is all about.
Khan aside, this guy is also really good.
http://www.youtube.com/watch?v=EX_is9LzFSY&p=C9298085590E88D5&playnext=1&index=15
even if you arent wonderful at the equations i think the concepts contained within calculus are useful for helping you understand things in everyday life
yhelothar
Lifer
- Dec 11, 2002
- 18,409
- 39
- 91
DrPizza
Administrator Elite Member Goat Whisperer
Whether it's better to put the creamer into the coffee at McD's, or whether it's better to put the creamer in the coffee when you arrive at work where you intend to drink it.
I used calculus to facilitate the cooking of venison summer sausage to calculate the remaining time, so I didn't have to probe the meat every 10 minutes for 2 or 3 hours.
Your examples certainly do not match schneiderguy's general form. On one there is a constant as the exponent on your first one it is the variable. On the next you have a constant as the entire function.
Gibson486
Lifer
- Aug 9, 2000
- 18,378
- 2
- 0
Fournier.... transform?
AHHHHHHHHHHHHHHHHHHHHHH
<runs screaming from room>
The equation just looks bad.
Fourier is actually very easy....just remember, Euler is your best friend and remember the rules regarding exponents with regards to integration.
NikolaeVarius
Lifer
- Oct 25, 2006
- 11,036
- 11
- 91
Really? My calc 1 professor taught the fundamental theorem the first day of class.
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