Self-Studying Calculus: Tips for Success from a High School Book

[TheKracken]

Could anyone give me some tips on self studying? I have a Calculus book from my high school ( I am alloud to use it for the remainder of the year...but I am NOT in calculus) So could anyone give me some tips on selfstudying skills, it would be extreemly helpfull, I just started on chapter 1 and it seems to just be a review of number lines with an introduction to the distance formula...but I just got to the equation of a circle and have never learned that, and still trying to comprehend what it is, but I am sure I will get it soon enough...but ya, tips please?

 

[victor.raum]

You're more likely to get replies if you improve your spelling, grammar, and punctuation skills first.

 

[Highway]

kahnacademy.com (.org?) for youtube video lectures, ocw.mit.edu for lecture notes / practice exams

and then go buy a book like this for the course materials explained in layman's terms: https://www.amazon.com/dp/0070434085/?tag=pfamazon01-20 -- it's literally 1 penny, and then $3.99 for shipping. it helped me through all of my calc courses.

 

[BloodyFrozen]

You might want to refresh on your precalculus skills.

 

[DivisionByZro]

You might want to refresh on your precalculus skills.

I second this statement. If you don't know the equation of a circle, chances are you also have many more gaps. Bridge those gaps as soon as you can. Worry about calculus after. Good luck!

 

[AnthroMecha]

The equation of a circle should be covered in Geometry, so if you haven't been through geometry I assume you probably haven't taken Trigonometry yet either. I wouldn't mess with Calculus until you've taken Trig.

 

[TheKracken]

I have taken geometry, and we have not gone over the equation of a circle (we have done the area and such...) As for trig I am currently taking trig, and I will agree that my spelling/grammar skill are not very good, but still, please serious answer's only. And I intent on filling in my pre-calculus necessitys as I go

 

[AnthroMecha]

I would strongly suggest pre-cal if you can take it. It helped me A LOT in Cal I, Cal II, and I'm sure Cal III next semester. And if you're in Trig I would hope that the professor mentioned that the unit circle is based on the equation of a circle.

 

[TheKracken]

I haven't learned anything of the unit circle yet :P
and I will be taking pre-calc over the summer at the local community college and was hoping to get ahead a bit and start learning calculus...as I have heard you don't really need pre-calc to do calculus

 

[AnthroMecha]

You don't need it, but you'll be at an advantage over those that didn't take it. It was basically a run through of Cal I-Cal III basics in my class, and it helped me when it came to the harder aspects of Calculus to already have a basic understanding. Make sure you don't take your attention away from Trig though, because you will use it a lot in your 4 semesters of Calculus. I used it a lot on Cal II this semester.

 

[USN2ENG]

http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

Check out this website, it was great and very thorough.

 

[AlephZero]

And if you're in Trig I would hope that the professor mentioned that the unit circle is based on the equation of a circle.

Nah... if advanced stuff like that isn't going to be in the final test, then you don't need to know about it

 

[Nano-Passion]

You don't need to know trig until after around chapter 3.2 depending on your book. Start the book now and you can learn whatever you need as you go along. And don't use those crappy Bob Miller books or any of the "books for dummies" series. I doubt you will learn anything from the material else than a very watered down experience. What you need to do is start! You will be fine, all you really need is some solid algebra IMO, and if you have that then you will blast through everything fairly easily. You can learn the trig as you go along.But First before I give further advice, I want to ask you something very important.. What is your plan of study? ie, what type of problems you will do, will you take notes, etc..

 

[TheKracken]

This was sort of why I was asking Nano..As i Wasn't sure what my plan of action would be. But, what I was thinking was basically just read the chapter and at the end of every section there are review problems and I would just do most of the odd problems for practice as the answers are in the back. I would do this pretty much whenever I have time so about 4 days a week for a few hours each time, and I have a teacher I can go to if I get extreemly stuck. The Book I'm using is Calculus 6th edition by larson, hostertler, and edwards...it seems decent, but If you have a different recomendation go right ahead,m I'm just barrowing this from the school.

 

[Nano-Passion]

This was sort of why I was asking Nano..As i Wasn't sure what my plan of action would be. But, what I was thinking was basically just read the chapter and at the end of every section there are review problems and I would just do most of the odd problems for practice as the answers are in the back. I would do this pretty much whenever I have time so about 4 days a week for a few hours each time, and I have a teacher I can go to if I get extreemly stuck. The Book I'm using is Calculus 6th edition by larson, hostertler, and edwards...it seems decent, but If you have a different recomendation go right ahead,m I'm just barrowing this from the school.

You mean 5th edition right? It is the latest, and the one I have. I'll try to break it down to what would be helpful for you..

1) Read the chapter slowly! Math shouldn't be read like biology, and in calculus you will be introduced to several new concepts.
2) Try to get a very good understanding of the concepts introduced to you. You can use other materials, and in fact, it would be recommended if you have another book to supplement your study with in case you get stuck.
3) You can take notes on the chapter, this forces you to read it slowly and really think about the theorems at hand.
4) Make sure you understand the theorems to be presented, as per axioms in algebra, you will use these to solve all the problems that ensue.
5) Do the proofs! Why not? You will get an appreciation for the mathematics and it will actually help you with the problems because you will understand why things are the way they are. If you understand why, everything follows really easily. I can see this in my class, where it is really obvious they have a superficial understanding because they will get questions wrong that I would contend are really easy.
6) Do lots of practice problems, but do it in a way that you should only do what you think would challenge you. If you see the basic concepts repeated over and over in the problems, and you see that it is way too easy, then look for something a bit different. For example, if they introduce something you think might trick you.
7) Do word problems! They will challenge your intimacy with the concepts that were introduced. Plus, they will likely be on future tests.
8) Work out some of the proofs in the problem sets, they are fun. Make sure you look up a few proofs first so you can get the feel for how to tackle them, unless you are already familiar.
9) Be careful when you work out the problems, sometimes you will be prone to silly algebraic mistakes when you go too fast.
10) Use cramster! <-- Invaluable tool for success. ;) Use it if you get things wrong, it will help pinpoint your mistake/loophole in your understanding.

That is about it, hope it helped. ^.^ I picked up a lot of these things through many wasted hours and trial and error.

 

[Jimbo57]

I'm doing the same thing although for credit. The online course I'm doing has a study guide that helps you along. I too skipped pre-calc (unit circle? who needs it?) and so what I did was I purchased a used pre-calc book online and anytime I encountered something that it sounds like I should know, I would go back and read up on it. Now I know the unit circle better than I know myself... If you're just using a textbook I'd say slowly go through it doing all the problems that correspond to the topic you just learned and if you encounter something unfamiliar, go back to a pre-calc text and read up on it, that or khanacademy.org

 

[BloodyFrozen]

If there was one thing I had to suggest, I'd say learn your trigonometry first. You HAVE to know the basic properties. I self-studied geometry and precalculus/trig, but when I got to calculus, it was necessary to know your trigonometry very well. Even though introductory calculus was easier than trig, you don't want to be stuck on the basic concepts taught to students before calculus. It was there for a reason.

 

[TheKracken]

You mean 5th edition right? It is the latest, and the one I have. I'll try to break it down to what would be helpful for you..

1) Read the chapter slowly! Math shouldn't be read like biology, and in calculus you will be introduced to several new concepts.
2) Try to get a very good understanding of the concepts introduced to you. You can use other materials, and in fact, it would be recommended if you have another book to supplement your study with in case you get stuck.
3) You can take notes on the chapter, this forces you to read it slowly and really think about the theorems at hand.
4) Make sure you understand the theorems to be presented, as per axioms in algebra, you will use these to solve all the problems that ensue.
5) Do the proofs! Why not? You will get an appreciation for the mathematics and it will actually help you with the problems because you will understand why things are the way they are. If you understand why, everything follows really easily. I can see this in my class, where it is really obvious they have a superficial understanding because they will get questions wrong that I would contend are really easy.
6) Do lots of practice problems, but do it in a way that you should only do what you think would challenge you. If you see the basic concepts repeated over and over in the problems, and you see that it is way too easy, then look for something a bit different. For example, if they introduce something you think might trick you.
7) Do word problems! They will challenge your intimacy with the concepts that were introduced. Plus, they will likely be on future tests.
8) Work out some of the proofs in the problem sets, they are fun. Make sure you look up a few proofs first so you can get the feel for how to tackle them, unless you are already familiar.
9) Be careful when you work out the problems, sometimes you will be prone to silly algebraic mistakes when you go too fast.
10) Use cramster! <-- Invaluable tool for success. ;) Use it if you get things wrong, it will help pinpoint your mistake/loophole in your understanding.

That is about it, hope it helped. ^.^ I picked up a lot of these things through many wasted hours and trial and error.

Thank you very much Nano, and everyone else that replyed to this topic, it was much appreciated. I intend to get another book to suplement my current and I can't wait to learn lots, i just got started on limits, and after trying to wrap my mind around it for an hour i finally got it, oh and as for the equation of a circle, i understand it now, just needed to think about it for a bit. Again thank you everyone. The person who skipeed pre-calc and is taking an online calculus course could you direct me to the website your using please?

 

[Nano-Passion]

Thank you very much Nano, and everyone else that replyed to this topic, it was much appreciated. I intend to get another book to suplement my current and I can't wait to learn lots, i just got started on limits, and after trying to wrap my mind around it for an hour i finally got it, oh and as for the equation of a circle, i understand it now, just needed to think about it for a bit. Again thank you everyone. The person who skipeed pre-calc and is taking an online calculus course could you direct me to the website your using please?

Anytime. :) Feel free to message me for any questions at any given moment.