How to teach myself pre calc, trig, and Calc 1?

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At a college level, using college level text?

I know this is really random but this summer I want to learn how to do college level calculus. I figure I will need to teach myself precalculus/trig and then move on to Calc I.

Does anyone recommend certain textbooks? I want to buy a really good one. A college leveled one.

Don't answer this if you are going to argue with me. My question is pretty straightforward.
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I am not going argue but, offer a suggestion. Why not enroll in a community college math course over the summer?
 
El Nino said:
I am not going argue but, offer a suggestion. Why not enroll in a community college math course over the summer?
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Oddly enough, my local CC doesn't offer summer programs to high school students. Do you recommend any books?
 
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jefgreen said:
Oddly enough, my local CC doesn't offer summer programs to high school students.
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...Are you sure? I've never heard of something like that. Maybe they won't let you use the credit towards high school/your gpa, but I can't see them outright not letting you take it.

As for books, I've never found any good ones. Why the rush to learn the math that quickly?
 
Jeff dude yo bro man, I think you should review Algebra I and II and to make a solid back ground before moving on. And then take Trigonometry (It's like Triangles, Circles, Graphs having sex together at the same time.), and take Calculus (Different concept at all).

That's my 2 cents. Peace out.
 
tennisball80 said:
Jeff dude yo bro man, I think you should review Algebra I and II and to make a solid back ground before moving on. And then take Trigonometry (It's like Triangles, Circles, Graphs having sex together at the same time.), and take Calculus (Different concept at all).

That's my 2 cents. Peace out.
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I agree. Going from Algebra2---> calculus in one summer is quite a big step.
 
Gotta agree with the last two people. Teaching yourself math, a subject that constantly builds on itself, is going to be damn near impossible without a solid foundation. Master algebra, and then see how trig goes. Baby steps, Jeff.
 
I also agree with everyone else. You've got to pace yourself, Jeff. I fear you're trying to get yourself involved in too many things, most of which are beyond your current level. I commend you for being so anxious to better yourself, but that desire shouldn't hinder you in the process.
 
hey jefgreen, i understand where you're coming from. i love your enthusiasm, and hopefully it will stay with you for good.

i once tried teaching physics to myself. got myself a good book.

it was quite hard. lol.
nothing like being taught by an instructor.

but if you truly want to study on the side, i guess you could get a book/books from your school, study section by section, and when you have questions, go to an instructor after school.

definitely not something most people do.

edit: i realize you want a college level book.
just keep in mind, in college mathematics has a broad horizon and finding the right book covering those ranges probably isn't possible. math and science come step by step. i recommend getting a high school book and mastering your basics, and maybe learning the next stages on your own. so i agree with tennisball.
 
Assuming the fact that you are pretty much good with Algebra, I would suggest you to review Algebra II in the summer and take Pre-Calculus in the next semester.

In that way, you can..
-Solidify your Algebra concepts
-Would not forget about math in the summer
-Get a head start comparing to your classmates
-Have a smart student impression for your teacher at the beginning of new semester
 
My school's pre-calc class uses "Precalculus with Limits" by Larson and Hostetler. And my school's calculus class uses "Calculus: Early Transcendentals" by Stewart. I basically learned everything I needed for calc through this book, and pretty much without any teacher/prof help, so it should work for you as well. However, I didn't use that pre-calc book, so I can't really say whether it is good or not. But it is a college level text, so it should be the type of thing you're looking for.

May I ask why you want to learn all this on your own though? You'll have plenty of time to learn this during school, whether it be in high school or college.
 
Pre-calculus is simple enough to teach yourself by reading the textbook and then doing problems. Same with trigonometry.

http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/VideoLectures/index.htm is a good place to learn calculus. Free video lectures from MIT so they are obviously not going to be easy. Calculus starts off hard with limits. That said, I know plenty of people who did well in calculus 2&3 with not understanding the foundations of calculus(limits).

For a textbook I couldn't say. The best ones are not in use and might be too unfamiliar in style for you.

If you are exceptionally bright I recommend: Spivak's Calculus

If you want a solid foundation with a classic: http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051/ref=pd_sim_b_11

If you read the reviews on either of them they will be blasting simpler books like Stewart. Take a look at the amazon preview and decide if the style suits you. I read Apostol after finishing calc3 in stewart and consider it far superior.
 
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gatorsbball said:
My school's pre-calc class uses "Precalculus with Limits" by Larson and Hostetler. And my school's calculus class uses "Calculus: Early Transcendentals" by Stewart. I basically learned everything I needed for calc through this book, and pretty much without any teacher/prof help, so it should work for you as well. However, I didn't use that pre-calc book, so I can't really say whether it is good or not. But it is a college level text, so it should be the type of thing you're looking for.

May I ask why you want to learn all this on your own though? You'll have plenty of time to learn this during school, whether it be in high school or college.
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Yeah, I've got that text if you are interested Jeff. But seriously, just take the math courses at your highschool. Calculus really isn't that hard, but it will be extremely hard for you if you are not prepared for it and do not have a solid math background. If you try to learn it without a proper base, it won't stick at all. There is a reason they have math courses in high school in a particular order. There are enough year to take each course, so there is no need to teach yourself one or more of them over a summer.
 
jefgreen said:
Oddly enough, my local CC doesn't offer summer programs to high school students. Do you recommend any books?
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I think you are incorrect on this. Community college is available for everyone.
 
I've heard lots of people who say pre-calculus (both the trigonometry portion and the algebra portion) is not necessary to learn calculus. Basically all the trig you need, you'll be taught again in calculus. However, if you don't even have a foundation in Algebra II, then I really don't know....

Anyways, take a look at CLEP tests and see if you're college accepts them. You could basically take the exam and receive credit for pre-calculus or at least advanced placement into calculus I depending on how your colleges accepts CLEP exams (assuming they do at all, which most all do).

I know you're not asking for it, but I'm gonna tell you something you've probably heard before: College and the pre-medical ordeal is a marathon, and very very long but very do-able task. Patience and fortitude is going to serve you much better than anything else. When in doubt err on the side of caution and convention and make sure you understand all the pre-req's before you jump into something so you can never start out behind. 🙂
 
That being said, never never never listen the elite-est people who talk smack about how impossible getting into medical school is. That's sometimes the biggest challenge.

But yeah:
1. I'd go for the CLEP exam, look at Barnes and Noble for CLEP exam reviews for pre-calc, I've seen many of them around. That way you can at least get future college credit for learning the Pre-calc.

2. Alternatively, why not talk to a math teacher at your HS and let them know your plan. They could give you a syllabus to use and maybe notes (if not, get them from an upper-classman) and perhaps you could use their book?
 
Dude, med school is extremely hard to get into. What are you talking about? After all the self-selection that takes place, still only about 40% of applicants get accepted. If you don't work your butt off in college, you probably aren't going to get in.
 
Hahahaha seriously. I love that. Please go on Pre-Allo and tell them how easy getting into med school is. It would be SO entertaining.
 
MilkmanAl said:
Dude, med school is extremely hard to get into. What are you talking about? After all the self-selection that takes place, still only about 40% of applicants get accepted. If you don't work your butt off in college, you probably aren't going to get in.
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😀👍👍👍
 
I am currently in pre- calculus and i have the best teacher ever.
And, trust me, without a teacher, you won't learn the theory behind all the math. You will only learn to do the problems.
My teacher tells us that if you don't learn the concepts of trig-- not just how to do the problems-- you will not have a good calculus year.

And, besides, if you are a freshman or sophomore, whats the rush? take it next yr
 
Strivetosucceed said:
I am currently in pre- calculus and i have the best teacher ever.
And, trust me, without a teacher, you won't learn the theory behind all the math. You will only learn to do the problems.
My teacher tells us that if you don't learn the concepts of trig-- not just how to do the problems-- you will not have a good calculus year.

And, besides, if you are a freshman or sophomore, whats the rush? take it next yr
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Believe what you want but calculus stands independently of trigonometry.
 
True. You'll obviously never learn how to integrate and differentiate trig functions without some trig, but you can do everything else (which is all you really need anyway).
 
Hey brother, thats great that you want to get ahead in your classes,
I had to do something very similar with chemistry, I think you should pick up some Cliffnotes books, they are cheap <$20, and cover the basics, ( does not go AS into detail as school text books)
 
I know you guys have given me some great responses and I appreciate it but I am still on the fence about what to buy. What do they use at MIT or Harvard for Calc I? I need a really good college leveled Calc I textbook. Not only that, but it should come with some extra materials, and a CD at least. In addition, can anyone suggest a GOOD workbook or something so that I can practice? I'm really serious about doing this.
 
I agree with the people saying you should study calc last.

Calculus, believe it or not, is easy. It's the Algebra and Trig that are needed to go along with it that are hard. If you can get a good background in Algebra and Trig and start to really know your stuff in and out, you'll have no problem with calculus. Calc is pretty much just manipulating equations and things using algebra and trig, and then just applying the Calculus formulas and things to them. It's hard to explain, but when you actually do it, you'll see what I mean.
 
I taught myself calculus in high school. It can be done. You need to be good at algebra and trig for it. And definitely geometry. You do not need pre-calc for it; that course has lots of advanced and useful things in it, like matrices, that aren't going to show up in Calc I. And a calculus book will teach you its own fundamentals, like limits, at the beginning, rather than as the last month of high school pre-calc. Limits are a complete change of topic and unrelated to the rest of pre-calc and it messes with high-schoolers in pre-calc because they're no longer building on the foundation they've been given all year.

Go to a bookstore and get a used college calculus textbook for $5. Check the table of contents: if it goes up to differential equations, it will cover you all the way through a Calc III course in college. Check the inside front and back covers for formulas from geometry, algebra, and trig, and maybe there will be derivatives and other things there that are calculus proper. OR you could have a long, numbered integral table. Check the appendices. They might explain pre-calc material back there, like the above-mentioned matrices, as well as other bonus material and proofs. It will have the integral tables, or the formulas instead if the tables were in the endpapers. And definitely make sure you've got the answers to odd-numbered questions, because no one is going to be checking your work but you.

Calculus is more about problem-solving skills and teaching you to think than the branches of mathematics you've had so far. You've seen word problems, but they're not like revolving an area around an axis and being told to find the volume of the resulting solid, when there are multiple methods, some appropriate and easy and some leading to unsolvable intermediate steps. If you're going to teach yourself, do it out of love for mathematics and not just to get ahead on medical school dreams.
 
No offense man, but I reiterate, you aren't going to jump from struggling with algebra 2 to being able to do calc over night. People already suggested books, read up. But honestly, it is a waste of time. Take the courses your high school gives you.
 
physics junkie said:
If you are exceptionally bright I recommend: Spivak's Calculus
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I seriously love Spivak. His proof on how 17 is the only "random" number was priceless. Plus that man's hair..wow. Just wow.

Seriously, though - there is a huge difference between reading a textbook and understanding the concepts well enough to actually learn the material. I would check with your community college again or at the very least find a course online that will force you do to problems to reinforce what you're learning.

As for your plan to cover so many courses at once...I don't think you would devote much time to any of them if your goal is just to get through as quickly as possible. If you really want to learn calculus, just focus on calculus first and leave the others for later. As I said above, just make sure that you actually work through problems, or what you read may filter back out of your head as quickly as it filters in.
 
URHere said:
I seriously love Spivak. His proof on how 17 is the only "random" number was priceless. Plus that man's hair..wow. Just wow.

Seriously, though - there is a huge difference between reading a textbook and understanding the concepts well enough to actually learn the material. I would check with your community college again or at the very least find a course online that will force you do to problems to reinforce what you're learning.

As for your plan to cover so many courses at once...I don't think you would devote much time to any of them if your goal is just to get through as quickly as possible. If you really want to learn calculus, just focus on calculus first and leave the others for later. As I said above, just make sure that you actually work through problems, or what you read may filter back out of your head as quickly as it filters in.
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http://www.stewartcalculus.com/

My cousin who is in College used a Stewarts Calculus textbook for Calc I. Has anyone else used one of these? Which one should I buy? Is it college leveled?
 
jefgreen said:
At a college level, using college level text?
Does anyone recommend certain textbooks? I want to buy a really good one. A college leveled one.
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Calculus Concepts and Applications by Paul Forester

I would stay away from Stewart Calculus, because not many examples for those who don't know how to do calculus yet
 
jefgreen said:
Spivaks "Calculus" book is used to teach freshman Calc I Honors @ OSU apparently.
/quote]


No it isn't. I did honors calc and we used Stewart's. Want to buy me old book? Hah. But seriously, I don't think you are making a good decision here. You aren't going to be able to learn calculus by yourself if you had trouble doing algebra 2 by yourself (due to a bad teacher). Just sign up for math classes in your high school and maybe do some at a community college if you can during high school.
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Also, what is a good Calculator to use? I use Texas Instruments'

TI-84 Plus

But my friend in AP Calc says that there are better ones to use out there.
 
Maygyver said:
jefgreen said:
Spivaks "Calculus" book is used to teach freshman Calc I Honors @ OSU apparently.
/quote]


No it isn't. I did honors calc and we used Stewart's. Want to buy me old book? Hah. But seriously, I don't think you are making a good decision here. You aren't going to be able to learn calculus by yourself if you had trouble doing algebra 2 by yourself (due to a bad teacher). Just sign up for math classes in your high school and maybe do some at a community college if you can during high school.
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Hey, its from wikipedia. I should have said take it with a grain of salt. My cousin @ kentucky uses the same book you use. Lots of colleges use it I think.

If you are serious about the book thing, sure, I'll buy it from you. If you include HW/Notes, and stuff.

I hear you. I plan on brushing up on my Algebra before I move on to any Calc I+ material. I have yet to call the community college. They might have something.
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jefgreen said:
Also, what is a good Calculator to use? I use Texas Instruments'

TI-84 Plus

But my friend in AP Calc says that there are better ones to use out there.
Click to expand...

A calculator really isn't a necessity for students learning math at a calc level or above (heavy "number" work is usually over by precalc). Sure, there are calculators out there that will compute integrals and the like for you, but if you want to learn, YOU SHOULD NOT USE ONE. Those calculators will give you the answer without helping you understand anything. Just rely on your head instead.
 
Look, if you want to learn calculus the right way pick up Tom Apostol's Calculus.

All these books like Stewart are so lacking in conceptal coverage of calculus that people who learn from them still don't understand limits by calc2. I wish I was kidding but my calc2 professor at USC(top 10 engineering school and all engineers take this) didn't even bother trying to teach us delta-epsilon proofs for two dimensions because we didn't understand them for one dimension...even though the proof is the the whole reason that calculus works!

Calculus used to be taught in sophomore/junior year in college. Then they started teaching it to freshmans. Then high school students. This happened from the 50s->70s. The result? Lots of finish calculus with A's who don't understand the first thing about it.

If you have genuine interest go slowly and learn it properly. Evaluating integrals and derivatives is easy. You just pull out Mathematica or your TI-89 and input them.

Learning it properly is the difference between being a radiologist and a radiology tech.

I have no idea why you would want to focus on the stuff you're going to learn anyways(Stewart's calculus-for-infants) when you could learn things that you would otherwise not have known that will give you deep insight into what you will learn in the future.

It is ironic that the foundations of calculus are considered too difficult so we avoid teaching them. The reality is that students are so convinced that mathematics is about doing algebra and geometry that they are resistant to learning something that doesn't involve doing math. The average student focuses too much on methods and not at all on theory. A damn shame.
 
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Jeff, could you please explain your CC's policy on high school students taking courses? We don't understand why you say they wouldn't let you, CCs usually take anyone who'll pay up.
 
TI-89s are the EZ Button for calculus. I am home for Spring Break so I will see if I have my exams from calc. Got 100s or close to it on both (1 might have been a 99 I think)
 
jefgreen said:
Also, what is a good Calculator to use? I use Texas Instruments'

TI-84 Plus

But my friend in AP Calc says that there are better ones to use out there.
Click to expand...


That's a nice tool , I've used it for such types of math works great however I'll have to purchase a new one cause the batteries exploded in it one summer 😳
 
Are the TI-89's basically what everyone uses? Because that is what I am hearing. I read a thread on here a while ago discussing this.

If I WERE to teach myself Calc, would the TI-84 be good enough until I can buy a TI-89?
 
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jefgreen said:
Are the TI-89's basically what everyone uses? Because that is what I am hearing. I read a thread on here a while ago discussing this.

If I WERE to teach myself Calc, would be TI-84 be good enough until I can buy a TI-89?
Click to expand...

Keep in mind that TI-89 is prohibited during ACT test.
 
jefgreen said:
Are the TI-89's basically what everyone uses? Because that is what I am hearing. I read a thread on here a while ago discussing this.

If I WERE to teach myself Calc, would the TI-84 be good enough until I can buy a TI-89?
Click to expand...

You DO NOT need, and absolutely should not use, a calculator to learn calculus.
 
You won't learn it as well if you use a TI-89... a lot of college Calculus classes don't even allow calculators at all so it could actually put you at a disadvantage when you get to college.
 
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