Calculus II and Beyond: How Much Harder?

[h00zah]

when going into university and completing first year calculus, how much harder is the proceeding levels of calculus, as in, are the concepts and methods just as hard to understand, or is it the same as calculus I all over again as if you have never seen calculus before?

 

[Metahominid]

I imagine Calc 3 = Multi D and Calc 4 = Differential Equations. Either way, it is really a matter of the individual. There are very few new concepts, if any really, that are added with each level.

Instead, Calc 2 extends 1 by building upon integration and differentiation, for me it was about as difficult but really all you are doing is using algebraic tricks for making integrals easier to solve.

Multi-D is what it says and considers the idea integration and differentiation of functions of more than one variable. Multi-d tends to be taught with the many physics examples because the mathematics is ideal for solving a great deal. Additional concepts are really just vectors.

Differential Equations is not much like the others except for that you use integration and differentiation to solve many things, however it is heavy on algebra.

In short, advancement is not really a matter of any crazy new concepts or more complex problems, many are very simple yet require more work and the chance for error increases. Setting up some problems can be difficult in multi-d once you are doing triple integrals requiring polar substitution, and problems applying Green's and Stokes theorems can get a little difficult.

 

[h00zah]

okay, thank you, that is a great reply and what I was thinking.

 

[Metahominid]

Yeah, as long as you understand pre-calculus (exponentials, trigonometry and logarithms), do your homework thoroughly and aren't afraid to ask questions then you should be good. You don't have to but it can be useful to have a study group of a few friends and getting to know your teacher's expectations for exams is key as well. Your will likely have different professors and each will explain in their syllabus how they grade exams and what they look for. Some may ok with skipping elementary steps while others wish for you to outline everything. Also it is nice because often Calc 1,2 and Multi D are all contained in one book, and hopefully you get to use it thoughout. If your professor did advise getting the solution book (almost all have a solution book) then it may good.

 

[h00zah]

My calc teacher in Highschool mentioned a book with a lot of calculus problems in it with the solutions, any idea what book this might be? It had like 1,000 problems. Wasn't so much a textbook as it was a problem/solution book.

 

[Metahominid]

I have no idea about that. My textbook, University Calculus by Hass Thomas Weir is nearly a thousand pages and probably has more problems than that. I'd probably google it or something

 

[Null_]

Instead of starting a new thread, I'll just ask here..

What level of calculus does Spivak's Calculus correspond to?

 

[Metahominid]

I am not really familiar with this author but it appears he has written a number of books of varying levels.

 

[sponsoredwalk]

Spivak is pretty crazy & unless math just flows like water for you I'd advise you to follow what Spivak says about his book being designed for students who have already completed the calculus sequence.

Don't just take my advice though, read the forums & see how highly it's praised & then see if my advice matters

I have Thomas & Weir Calculus & I must say it's only okay at best.

If I had the chance again, I really would have bought this astounding book:

https://www.amazon.com/dp/0871503417/?tag=pfamazon01-20

It's only 50 cents!

(well, not really because you have to pay for
postage too, but like $4 isn't bad!).​

I look in it & it clarifies so many things so quickly & so intuitively.

It is from the 80's, which means it doesn't assume your an idiot & has 30 questions per chapter that help instead of 100+ that nobody has time for.

 

[Metahominid]

Ha, I have Swokowski's, took it when I was in high school. Never returned it.

 

[Null_]

Hm, thanks for the suggestion! I may pick up a copy to have alongside Spivak. I've always felt buying a used textbook is a much better use of $4-5 than a Starbucks frap! :P