Calculus 1 (I'm taking the class in a week.)

[ME_student]

I am finally getting my feet wet, actually taking math courses that apply to my degree. Anyone have any suggestion what I should be studying before I take the class?

I have borrowed a book from a local library called "Calculus Essentials for Dummies." I have a friend who is in calc 3, I think. He recommend I memorize the unit circle and trig identities. I am supper stoked! I can't wait to take this class!

 

[BloodyFrozen]

Be comfortable with College Algebra/ Algebra II topics and trig like your friend said.

 

[Mandlebra]

Make sure you are comfortable with algebra and arithmetic!

 

[Millennial]

Well, memorize some trigonometric function values and trigonometric identities. They often come up when you have to simplify expressions. Also be comfortable with algebra as well. That's about it.

 

[ME_student]

Okay thanks. I should probably study up on some basic algebra. I noticed when I took college algebra and trig I sort of struggled with a few simple algebra rules... Like multiplying both top and bottom with a conjugate or eliminating the square root sign from the denominator or knowing that X^-3 is 1/X^3.

 

[ZenOne]

Don't worry--Calculus 1 is cake, if you're excited and willing to put in the work you will end up loving it.

 

[seaofghosts]

Calculus itself is extremely easy. The hard part is remembering trig and all the little algebraic tricks that have inevitably been forgotten since those classes were taken (it's been three years for me). So try getting one of those "trigonometry in 10 minutes" books (or whatever they're called), and perhaps algebra as well.

 

[Chunkysalsa]

Yea most of the time in Calc 1, the easy part of the problem is the calculus (taking a derivative), the rest of the problem is more or less algebraic simplification. People who struggle with calc 1 are the ones who are bad at algebra. (This actually goes for a lot of subjects)

 

[mathwonk]

most mathematicians think calculus was the hardest course they ever took. that is probably because they tend to take honors level versions that are very rigorous. in non honors calculus, the gatekeeper is ALWAYS algebra skills. memorizing formulas does not help. skill in manipulating expressions is the essential. exactly what chunkysalsa and others said. I taught university calculus for over 35 years at every level, from first semester to graduate analysis.

 

[ME_student]

Calculus itself is extremely easy. The hard part is remembering trig and all the little algebraic tricks that have inevitably been forgotten since those classes were taken (it's been three years for me). So try getting one of those "trigonometry in 10 minutes" books (or whatever they're called), and perhaps algebra as well.

Same here.

I had recently taken trig, did pretty well. I actually did better in trig than college algebra. I bought my calc book yesterday looking through the book, noticed calc is very different.

 

[ME_student]

Yea most of the time in Calc 1, the easy part of the problem is the calculus (taking a derivative), the rest of the problem is more or less algebraic simplification. People who struggle with calc 1 are the ones who are bad at algebra. (This actually goes for a lot of subjects)

I am not necessarily bad at algebra. I just don't have a strong foundation in that era because the last algebra class I took was four year ago.

 

[seaofghosts]

I did better in trig as well, probably because things just finally started accumulating by that point. I'm taking calc (again, had to drop because of work before) in the fall, so I'm trying to catch up on all the trig and will probably at least go through Kline's Calculus before class starts.

 

[Windowmaker]

I don't think the trig identities are as important in calc 1 as they are in calc 2. Mostly of Calc 1 is limits, derivatives and basic integration. It's been a year since I had calc 1, but I don't remember needing a lot of trig, besides knowing what the integral of sin or cosine was. I know it pops up A LOT in calc 2.

 

[seaofghosts]

My calc 1 class had a LOT of trig. One of my friends who took the class at the same campus posted on FB, "I might as well just tattoo the unit circle on my arm..." I'm sure it depends a lot on the textbook and instructor you have, but I wouldn't skimp on the review just in case.

 

[ZenOne]

^^^Maybe you had a Calculus 1 and 2 joint class?^^^

Calculus 2 was trig heaven (or hell if you don't like it--I do) compared to calculus 1--in my experience, at least.

 

[seaofghosts]

I don't think so, it was the first of the standard three calc courses.

Of course, "a lot of trig" could mean a little once I see what's in calc 2, haha.

 

[krobben]

From my experience in all of the calc courses, this is all that matters...

1. WHO you learn from. Calculus is more about ideas/concepts where as college algebra is just rhetoric memorization. Who guides you in learning is everything in calc. If your professor is standing up there speaking total gibberish to you, then seriously consider substituting that time with a personal tutor or a different lecture professor. Calculus is so easy if its explained correctly. Khan Academy is probably your best friend for as far as tutoring goes. My experience from calculus was that lecture was straight boring and helpless and so was recitation. So I found a good book on calculus, learned from it and never showed up to another lecture or recitation in calc for all 3 courses did well on the exams and tests.

2. Know your basics. Seriously, don't waste your time with calculus if you can't score an 80 on a college algebra final right now. Yeah, you could skid through one hell of a bumpy semester with poor college algebra preparation as I've seen my friends do whereas I spent maybe 3 hours a week in every calculus course and most of it was on just the theory.

 

[andyroo]

Before you take the class, honestly knowing the main topics (WELL, possibly to memory) of pre-calculus and algebra 1 and 2 are essential, but refreshing yourself before and while you take the course isn't a bad idea (that's what I did when I took Calc 1 at least). Then, once you start, try to understand the reasoning of definitions and theorems intuitively. As far as calculations and knowing what to do with certain problems goes, it's important for you to know what you can do to the problem to solve it and also know WHY you can use such a method. For example, if given:

d/dx (sinx/secx),

you should know how to solve the problem based on what you know about the derivatives of sinx and cosx along with this tool called the product rule. This is pretty basic, but new material will build upon on material that you previously learn throughout the course. Problems can become increasingly complex near the second half of the course I'd bet, but so long as you keep up with new material and understand how everything works together up until the bitter end, you should do well. Also, memorization is a big thing in pretty much all math, so might I suggest using notecards with problems and solutions on the back a few days before any quizzes or tests?

 

[ME_student]

From my experience in all of the calc courses, this is all that matters...

1. WHO you learn from. Calculus is more about ideas/concepts where as college algebra is just rhetoric memorization. Who guides you in learning is everything in calc. If your professor is standing up there speaking total gibberish to you, then seriously consider substituting that time with a personal tutor or a different lecture professor. Calculus is so easy if its explained correctly. Khan Academy is probably your best friend for as far as tutoring goes. My experience from calculus was that lecture was straight boring and helpless and so was recitation. So I found a good book on calculus, learned from it and never showed up to another lecture or recitation in calc for all 3 courses did well on the exams and tests.

2. Know your basics. Seriously, don't waste your time with calculus if you can't score an 80 on a college algebra final right now. Yeah, you could skid through one hell of a bumpy semester with poor college algebra preparation as I've seen my friends do whereas I spent maybe 3 hours a week in every calculus course and most of it was on just the theory.

Thanks, I have been watching a lot of khan academy. I just started classes last night and I understand most of the material we went over. I don't really like my professors style of teaching though because she expects us to know a lot, too much. I was surprised how quick her lectures are... She lectures for two hours then we have lab for two hours, working in groups. She doesn't assign too much homework and most of the material isn't from the textbook which sucks. Her assignements are based off the material we worked on in lab.

 

[ME_student]

Before you take the class, honestly knowing the main topics (WELL, possibly to memory) of pre-calculus and algebra 1 and 2 are essential, but refreshing yourself before and while you take the course isn't a bad idea (that's what I did when I took Calc 1 at least). Then, once you start, try to understand the reasoning of definitions and theorems intuitively. As far as calculations and knowing what to do with certain problems goes, it's important for you to know what you can do to the problem to solve it and also know WHY you can use such a method. For example, if given:

d/dx (sinx/secx),

you should know how to solve the problem based on what you know about the derivatives of sinx and cosx along with this tool called the product rule. This is pretty basic, but new material will build upon on material that you previously learn throughout the course. Problems can become increasingly complex near the second half of the course I'd bet, but so long as you keep up with new material and understand how everything works together up until the bitter end, you should do well. Also, memorization is a big thing in pretty much all math, so might I suggest using notecards with problems and solutions on the back a few days before any quizzes or tests?

What is the purpose of different quotient? Basically you take a function and plug it into the formula to get a new function which allows to find a point on the graph?

 

[ChiralWaltz]

Calc I is differentiation and integration. You can start deriving while you are in the material you are currently in, if you're not already. Learn how to do derivatives before looking at integrals. Work enough problems to spit out the rules in your sleep.

here are the rules
google: table of differential formulas (I'm noob and can't post links)

another good site
google: patrickJMT

I hope you found this helpful.

 

[mathwonk]

there isn't much trig to know. the basic identity is sin^2 + cos^2 = 1.

if you want more you divide that one by cos^2, and get tan^2 + 1 = sec^2.

there are really only about one or two others.

sometimes you need the double angle formulas: sin(2t) = 2sin(t)cos(t),

and cos(2t) = cos^2(t) - sin^2(t).if like me you tend to forget these, you can recover them from the exponential version

i.e. cos(t) + i sin(t) = e^(it).

so cos(2t) + i sin(2t) = e^(2it) = [e^(it)]^2 = [cos(t) + i sin(t)]^2

= [cos^2(t) - sin^2(t)] + 2 i sin(t)cos(t). yep i got them right.

I am assuming here that you know the basic precalculus stuff like [e^a]^b = e^(ab).

that stuff is what really stumps more people.

 

[ME_student]

there isn't much trig to know. the basic identity is sin^2 + cos^2 = 1.

if you want more you divide that one by cos^2, and get tan^2 + 1 = sec^2.

there are really only about one or two others.

sometimes you need the double angle formulas: sin(2t) = 2sin(t)cos(t),

and cos(2t) = cos^2(t) - sin^2(t).


if like me you tend to forget these, you can recover them from the exponential version

i.e. cos(t) + i sin(t) = e^(it).

so cos(2t) + i sin(2t) = e^(2it) = [e^(it)]^2 = [cos(t) + i sin(t)]^2

= [cos^2(t) - sin^2(t)] + 2 i sin(t)cos(t). yep i got them right.

I am assuming here that you know the basic precalculus stuff like [e^a]^b = e^(ab).

that stuff is what really stumps more people.

Thanks, did a little bit of studying a few weeks ago. I have the unit circle memorized, including the special angles. Second day of class we discussed limits, continuity, and limits laws. I have been enjoying the class so far.

 

[Alex1]

How long does it take to teach yourself to learn calculus? I just graduated high school and have taken up to pre calc. It's summer now and I've recently started going to the library to try and learn more physics. Is it possible that I could have a strong foundation and the knowledge that would be acquired in a college level class in calc before college this fall?

 

[PhizKid]

there isn't much trig to know. the basic identity is sin^2 + cos^2 = 1.

if you want more you divide that one by cos^2, and get tan^2 + 1 = sec^2.

there are really only about one or two others.

sometimes you need the double angle formulas: sin(2t) = 2sin(t)cos(t),

and cos(2t) = cos^2(t) - sin^2(t).


if like me you tend to forget these, you can recover them from the exponential version

i.e. cos(t) + i sin(t) = e^(it).

so cos(2t) + i sin(2t) = e^(2it) = [e^(it)]^2 = [cos(t) + i sin(t)]^2

= [cos^2(t) - sin^2(t)] + 2 i sin(t)cos(t). yep i got them right.

I am assuming here that you know the basic precalculus stuff like [e^a]^b = e^(ab).

that stuff is what really stumps more people.

Learning Euler's formula helped me a ton to remember the double angle formulas

Is there anything similar to recall/derive the sum/difference formulas?

 

[Alex1]

Thanks man Ill try and get on that

 

[ME_student]

Calc I is differentiation and integration. You can start deriving while you are in the material you are currently in, if you're not already. Learn how to do derivatives before looking at integrals. Work enough problems to spit out the rules in your sleep.

here are the rules
google: table of differential formulas (I'm noob and can't post links)

another good site
google: patrickJMT

I hope you found this helpful.

Thanks, I watched a few videos off patrickJMT. Those videos were quite helpful.

 

[ME_student]

So far calc 1 has been pretty easy so far. We are making are way into integration.

I was working with a tutor today on an integration problem. Is it possible to take an anti-derivative of a function? That didn't make any sense to me when the tutor told me you can take anti-derivative of a function like f(x).

I thought you can only take an anti-derivative of a derivative function like f'(x)?

 

[micromass]

Learning Euler's formula helped me a ton to remember the double angle formulas

Is there anything similar to recall/derive the sum/difference formulas?

e^{i(a+b)}=a^{ia}e^{ib}

Now express these things in sines and cosines.

 

[ChiralWaltz]

I thought you can only take an anti-derivative of a derivative function like f'(x)?

Not necessarily true. It depends on what the function is. Derivatives and anti-derivatives are rules that can be applied to functions. Some functions will allow you to derive/anti-derivative more than once. Integration is where your anti-derivative practice is going.

Look at the chain rule if you haven't had a chance yet.

 

[ME_student]

Not necessarily true. It depends on what the function is. Derivatives and anti-derivatives are rules that can be applied to functions. Some functions will allow you to derive/anti-derivative more than once. Integration is where your anti-derivative practice is going.

Look at the chain rule if you haven't had a chance yet.

We are not allowed to use the chain rule yet. We are still manipulating our functions and derivatives by graphing it.

I recently learned how to take a function and draw a tangent slope barely touching the function. Then using rise/run to get a slope. Another graph I would trace the lines out getting my derivative of the function.

How do I approach anti-derivatives by graphing?

 

[ME_student]

From my experience in all of the calc courses, this is all that matters...

1. WHO you learn from. Calculus is more about ideas/concepts where as college algebra is just rhetoric memorization. Who guides you in learning is everything in calc. If your professor is standing up there speaking total gibberish to you, then seriously consider substituting that time with a personal tutor or a different lecture professor. Calculus is so easy if its explained correctly. Khan Academy is probably your best friend for as far as tutoring goes. My experience from calculus was that lecture was straight boring and helpless and so was recitation. So I found a good book on calculus, learned from it and never showed up to another lecture or recitation in calc for all 3 courses did well on the exams and tests.

2. Know your basics. Seriously, don't waste your time with calculus if you can't score an 80 on a college algebra final right now. Yeah, you could skid through one hell of a bumpy semester with poor college algebra preparation as I've seen my friends do whereas I spent maybe 3 hours a week in every calculus course and most of it was on just the theory.

I take back what I said about Khan Academy being a good source. He teaches calc differently than I am use to because when he applies chain rule he derives it from the inside out. I thought we are suppose to derive from the outside in.