Is Self-Studying Calculus 2 Over Summer a Good Idea?

[jsewell94]

Hello everyone!

Alright, my current high school math class is IB Higher Level Mathematics. It's a two year long course. During the first year we have focused primarily on Advanced Algebra, Trigonometry, and we are about to start Vectors. Year 2 consists of Calculus I, Statistics, and then we focus on our class "option" which, for us, is Sequences and Series and Differential Calculus.

So, seeing as how I will have a firm base in Calculus 1 by the end of my senior year, I was wondering if teaching myself Calculus 2 over that summer is a viable option? From everything that I have read, Calculus 2 is incredibly difficult which makes me think that independent study is next to impossible. I want to learn it independently because I'd love to test out of Calculus 2 my freshman year and jump right into Calculus 3.

Opinions? If you feel that learning calculus 2 independently is doable, then what books to recommend for doing so (for future reference)?

Thanks!
-Jacob

 

[micromass]

I'm sorry, since I'm not american, I don't know what calculus 2 is all about. Can you tell me it's contents?

But in general, I think any calculus is not impossible. You'll have to work for it and solve many exercises, sure. You'll have to use this forum a lot to ask all sort of questions, correct. But it is certainly not impossible to study on your own. I'm sure you could learn it with some work. And even if you don't: you'll be prepared for what comes next.

As for books, I'll have to see first what the contents of calculus 2 is. And you'll also need to tell what your major will be. Since obviously, a math major will need another book than a liberal arts major...

 

[jhae2.718]

I assume you mean integral calculus when you say "Calculus 2"?

While integration is nontrivial compared to evaluating derivatives, it shouldn't be difficult to self-study integral calculus.

 

[TylerH]

To those who don't know what Calc II is: Basically, it covers everything after integration by substitution to Taylor Series. The goal is for Calc I to cover the easy half of calc of a single variable(most differentiation and easy integration) and the second is to scare off the dumber soon-to-be engineers with super hard integration and other harder concepts. I think most universities split them, so it's easier for non-math/science majors to get graduate. Some take multiple attempts just at calc I, could you imagine how requiring calc II would affect the pass level?

If you look through a Calculus of a Single Variable class(like this one, at MIT) and learn the stuff you don't already know, you'll be done. I personally recommend those videos. I watched most of them(doing so like a real student, paying attention, taking notes, etc.) while still in Precal last semester. I entered Calc I, this semester, on an entry Calc III level, according to my professor. If you're really ambitious, watch the 18.02 videos too, then you'll be done with Calc III and some of Differential Equations.

 

[jhae2.718]

I think the equivalent course at my university also covers the basics of operations in [tex]\mathbb{R}^3[/tex].

But again, teaching yourself shouldn't be much of a problem. I pretty much taught myself calculus on my own in high school.

 

[Char. Limit]

Teaching yourself is not going to be a problem. If you ever come up with a problem, just ask us!

In particular, I've helped teach someone calculus when he had problems before.

 

[HeLiXe]

Opinions? If you feel that learning calculus 2 independently is doable, then what books to recommend for doing so (for future reference)?

Thanks!
-Jacob

Hi Jacob :)
I'm in calculus II now and I think that learning it independently is completely doable. In the very beginning of this course, I also thought that CalcII was incredibly difficult and a user on this forum recommended that I do a lot of problems. It worked out beautifully! What makes it seem difficult at first (in my case anyways) is that you are learning new methods for analysis while implementing them simultaneously, as you work through the methods by doing numerous exercises you get a handle on application, and analyzing and implementing becomes tremendously easy after that. Anyways none of that may apply to you, but just wanted to mention it in case it did.

I take my course online with no help from my professor. The lectures are from Prof. Edward Burger and are accessible through Thinkwell...I think the cost is $150 to access the course. The lectures are really helpful with concepts, but a supplemental text is necessary. I use Thomas' Calculus 11th edition. I started a https://www.physicsforums.com/showthread.php?t=439546" and other users recommended the first and earlier editions. Some of the concepts I am learning in calcII start as early as chapter 4 in this book and are intertwined with some of the things I learned in calcI, so for a "straight calcII" book I would recommend visiting the math learning materials section of PF and see if you can find anything there...maybe a section of a book is recommended.

 

[Femme_physics]

Thinkwell website has a very good calculus segment. It teaches you via videos, with a great teacher (Edward Burger)... Although, they also cover calc 1. They do cost.

You can self-study it for sure, but I find it hard to study math without having students around I can interact with. If you don't feel it could be a problem, go ahead.

 

[lavinia]

For me vector calculus came to life in Physics books. Feynmann's Lectures book 2 develops vector calclulus in the rich context of Electricity and Magnetism.

A good book on mechanics for engineers would also be good -

I like to learn by choosing a topic then learning the background as needed. This is often the Physicist's approach. But if you want to stay pure in mathematics then I suggest a basic book on classical differential geometry - e.g. Struik's book. You would need to learn some basics first - e.g. what is a partial derivative and how to integrate in more than one variable.

 

[symbolipoint]

Not having yet read the responses to this original post, I have a response:

Hello everyone!

Alright, my current high school math class is IB Higher Level Mathematics. It's a two year long course. During the first year we have focused primarily on Advanced Algebra, Trigonometry, and we are about to start Vectors. Year 2 consists of Calculus I, Statistics, and then we focus on our class "option" which, for us, is Sequences and Series and Differential Calculus.

So, seeing as how I will have a firm base in Calculus 1 by the end of my senior year, I was wondering if teaching myself Calculus 2 over that summer is a viable option? From everything that I have read, Calculus 2 is incredibly difficult which makes me think that independent study is next to impossible. I want to learn it independently because I'd love to test out of Calculus 2 my freshman year and jump right into Calculus 3.

Opinions? If you feel that learning calculus 2 independently is doable, then what books to recommend for doing so (for future reference)?

Thanks!
-Jacob

High school Mathematics courses as you told us may be useful preparation for Calculus 1 in college or university. Calculus 2, if for university/college, requires the equivalent skill and knowledge of Calculus 1 (and again, I mean for college level). You need to be strong in Algebra and Trigonometry.

You very well may find Calculus 2 to be incredibly difficult - the first time. Whether you self-study it or do it in a class does not really matter. If you know Calculus 1 material well, you can study Calculus 2, even if you study in the summer on your own. If you find it too difficult, then maybe it's because you are (still?) weak in Calculus 1; so study Calculus 1 again before trying Calculus 2 again. Any Math course, including Calculuses, that you study more than once, should be much easier the second time (well, maybe not "much", but "significantly").

 

[Stephen Tashi]

There is a difference between understanding and drill. You can understand how to do a given type of problem but not be able to do it as quickly as a person who has drilled at doing that type of problem over and over again. Most people who prefer the slow pace of self study don't like to drill at working problems that they already understand. People who take formal classes or study in groups are more likely to do drills and develop the speed and accuracy needed to do well on standardized tests.

In later life, outside the academic world, I think people who self-study perform as well as those who take formal classes. Both types of person will either forget the material through disuse or, if they employ it in their work, they will become practiced and drilled.

If you will face some standardized exams on you knowledge of Calculus 2, I suggest taking it as a formal course even if you do self-study.