Is Self-Teaching Calculus Possible and Effective?

[James2]

So, I am bored with Algebra 2 in high school and I've been teaching myself calculus and I've learned it pretty fast, well of course not all of it, but I am learning it quickly and grasping a lot of the concepts. So, is this an okay way to learn elementary Calculus? It really helps that the book I have is very well written. It's called "Technical Calculus with Analytical Geometry" -a Dover book by Judith L. Gersting. I also sometimes go to the math/physics/astronomy library at my local university(my parents work at that school) and learn a lot from their books. I will ask willing people about it as well, but I am not in a class, but when I do enter one I will be prepared because I've gone through a semester or so in a month or less and I've tested myself and it's pretty much second nature! What is the downfall to teaching myself like this?

 

[FalseVaccum89]

So, I am bored with Algebra 2 in high school and I've been teaching myself calculus and I've learned it pretty fast, well of course not all of it, but I am learning it quickly and grasping a lot of the concepts. So, is this an okay way to learn elementary Calculus? It really helps that the book I have is very well written. It's called "Technical Calculus with Analytical Geometry" -a Dover book by Judith L. Gersting. I also sometimes go to the math/physics/astronomy library at my local university(my parents work at that school) and learn a lot from their books. I will ask willing people about it as well, but I am not in a class, but when I do enter one I will be prepared because I've gone through a semester or so in a month or less and I've tested myself and it's pretty much second nature! What is the downfall to teaching myself like this?

In my experience, the biggest downfall to self-study is it being rather difficult at times to tell where the gaps in your knowledge base are.

 

[Mentalist]

I am not well versed in giving advice. But, in my personal opinion, it is a bad idea to neglect algebra, even if it is simple algebra 2. It is essential to know it, and then proceed onwards to trigonometry because trigonometry is essential in physics (I am taking relativity now, so we are more learning about reaction rates, decay, etc..., than using trigonometry but we did utilize it a bit in the beginning) and higher mathematics.

Neglecting an area for a higher area in the same "subject" is bad in my honest opinion, and if I were you, I'd focus most of my energy in learning/mastering algebra 2 and once that is completed move on to trigonometry and then calculus. After Calculus 1, physics.

I am basing this off of my personal experience so far, but that is what I did and I ended up doing well in all of the courses so far in college. You may just be smarter than I am, so, you do what actually is best.

For the book I used in Calculus it was Stewarts + Thomas/Finney. I've never heard of the book you're using though.

 

[seaofghosts]

I think the major downfall to teaching yourself calculus (or any math, really) is not doing enough problems. Classes kinda force you into it. But if you're using a good book with plenty of problems, like an actual college textbook, and you work EVERY problem, seeking help when you need it, then you can definitely teach yourself. Even if it feels like you're doing enough, college textbooks throw some weird stuff at you sometimes. One of my homework assignments for first semester calc took three full days to complete, and I mean 10+ hours a day. I thought I was going to die afterward, and dreamt in math. I still don't feel like it was enough.

That said, don't kill yourself on calc problems. Regardless of what you're doing now, understanding the concepts will definitely give you a head start when you take it either in HS or college. I really like "Calculus: An Intuitive and Physical Approach" (also Dover, I adore Dover) when it comes to actually GETTING calculus. There aren't many problems in it, but that's why I like it. I read that alongside my college textbook.

In an actual calc class, you're going to be working thousands of problems, using just about every algebra/trig rule you learned in previous classes, so make sure you're not skipping out on algebra while you study calc. :p

 

[jtpope2]

differential calculus and basic integration are pretty easy to learn on your own (i remember doing the same in high school). when you get to tougher problems in integral caculus, it'll help to have a teacher walk you through it. there are a lot of good lectures and problem examples on youtube which could help you a lot (mit courseware, patrickjmt). try to get as far as you can and you'll run circles around your classmates in calculus, good luck!

 

[James2]

Thanks guys, I've hit a snag on differentiation of trig functions; well like I get how the basic patterns work but then it becomes a cluster of confusion. (Especially with the power rule/quotient rules) What should I do to organize the problem better and reduce error?

 

[Robert1986]

Thanks guys, I've hit a snag on differentiation of trig functions; well like I get how the basic patterns work but then it becomes a cluster of confusion. (Especially with the power rule/quotient rules) What should I do to organize the problem better and reduce error?

OK, this makes sense. I was a little confused when you said you had made it through an entire semester in a month. As it turns out, you are nowhere near finished with what I would consider a normal semester - this is good because doing one semester of calc in a month is nearly impossible (espicially with self study.) To answer this question, just do more and more problems, then you will start to "see" how things work.

 

[Mdhiggenz]

Even though most high school math classes are a joke. I would still try and get as much as you can from algebra as possible. Most of the time the calculus is easy, it's the algebra that gets you!

 

[Studiot]

Take heart from George Green, young sir.

Green's background was too poor to undertake formal mathematical study or indeed any significant schooling.
He was self taught, from books.

That led him to propose some of the most important theorems in calculus and to revolutionise mathematical physics in his day.

Self learning calculus for fun because you are otherwise bored is fine so long as it does not lead to greater boredom when you come to this material in college, although this might spur you on to self study even more advanced stuff.

I look forward the the James Theorems one day.

go well.

 

[mathwonk]

i'll give you a clue as to what is considered standard in calculus courses, by those who have it mastered. differentiation of basically anything at all is considered to be dead easy, falling off a log, completely unchallenging. so unless you are at that point, you have a ways to go in teaching yourself.

if your algebra course is boring, try this one. i'll guarantee it this one will teach you something you do not know.

http://archive.org/details/elementsalgebra00lagrgoog

 

[James2]

Well in regards to one of the posts I saw earlier, I don't think I actually learned an entire semester, but it sure felt like it by the sheer amount of problems! Anyway, no, I am definitely not neglecting Algebra study at all. I do my homework the instant it is assigned and pay attention in class, I am annoyed that my teacher is skipping things though and told her I needed to learn certain things for calculus so it's best to know the entire book and she said "I can't teach every single thing in the book, there just isn't time and most kids don't care like you do." So yeah, that is a problem because it hurts my background when areas are skipped.

 

[FalseVaccum89]

Well in regards to one of the posts I saw earlier, I don't think I actually learned an entire semester, but it sure felt like it by the sheer amount of problems! Anyway, no, I am definitely not neglecting Algebra study at all. I do my homework the instant it is assigned and pay attention in class, I am annoyed that my teacher is skipping things though and told her I needed to learn certain things for calculus so it's best to know the entire book and she said "I can't teach every single thing in the book, there just isn't time and most kids don't care like you do." So yeah, that is a problem because it hurts my background when areas are skipped.

Study them yourself. There are tons of materials (both legitimate and not) on the Internet for most topics through the graduate sequence.

 

[James2]

Guys I'm actually stuck on an integration problem involving the "u du rule" thing. It's just a little confusing; just one question, if I take du do I add it to the other part of du or do I replace the other stuff that isn't in u?

 

[jtbell]

Ask here and give some more detail:

https://www.physicsforums.com/forumdisplay.php?f=156