Brushing up for Calc 3 - Concerns

[torquemada]

Hi I wanted to take calc 3 this summer and i want to start brushing up as I took calc 2 back in spring 08. I was wondering if there are infinite series in a typical calc 3 course? If so I need to brush up on them. Also concerning the laundry list of different integration techniques for the indefinite integral that we grinded through in calc 2 (partial fractions, u substitution, ad nauseum) - is it important to know all of those techniques cold for calc 3? Or is the general concept of the integral enough? thanks

 

[Chaostamer]

From what I've seen, Calculus III generally doesn't include any complicated integration techniques (which is a bit unfortunate, really). It's often likened to Calc I, which is an apt comparison because much of the material basically IS Calc I material in three dimensions (generally with the addition of vector calculus). It's harder than Calc II, but you shouldn't need more than Calc I knowledge to understand the class.

As for sequences and series, no, they're not included either. But then, that material really falls more under analysis than calculus anyway.

 

[torquemada]

From what I've seen, Calculus III generally doesn't include any complicated integration techniques (which is a bit unfortunate, really).

Thanks for the insight. I was wondering additionally, my laziness aside, why is this unfortunate?

 

[nlsherrill]

Thanks for the insight. I was wondering additionally, my laziness aside, why is this unfortunate?

What Chaostamer said sounds about right, however in my calc 3 class we did have plenty of examples where u-sub, integration by parts, etc. It wasn't quite as frequent as calc 2, but you should still be familiar with these techniques in general. Calc 3 really is quite different than 1 and 2. You will find that setting up your integrals will be the hardest part, and solving should be the easier part.

 

[Chunkysalsa]

I really liked Calc 2 but I currently really hate Calc 3, though we haven't even gotten to any multivariable calculus (and I have my doubts that we will even get too far). Its all been studying 3D space (planes, surfaces, etc) and vector valued functions.

I would take a look at some old calc stuff but the important thing is to realize when to use those techniques rather than how to use them. Its easy to look up something in a book if you know what you are looking for. I only took calc 2 last semester but find myself referencing some of those techniques that I've already forgotten how to do. (Though I do it mostly for my ODE class and not Calc3)

 

[General_Sax]

The only hard part about calc3 integrals is setting the limits of integration. After that it's pretty straight forward.

 

[S_Happens]

Like was already stated Calc 3 is mostly 3-dimensional calculus. In my course, there were no more infinite series. You learn some new vector operations (dot and cross product), a few other new operations (curl, gradient, etc.), double and triple integrals, but no new real integration techniques like calc 2. Personally I thought it was much easier than calc 2.

 

[Chaostamer]

Like was already stated Calc 3 is mostly 3-dimensional calculus. In my course, there were no more infinite series. You learn some new vector operations (dot and cross product), a few other new operations (curl, gradient, etc.), double and triple integrals, but no new real integration techniques like calc 2. Personally I thought it was much easier than calc 2.

I'll never understand that mindset. To me, Calc II was just a matter of figuring out a systematic method for evaluating integrals and series convergence (the two topics most people seemed to have the biggest issue with, at which point 95 percent of the problems became pretty straightforward. Calc III actually required us to understand the math at a higher, more conceptual level and demanded a lot more proof. Plus, I always thought that the multiple integrals and vector calculus sections were just tricky.

I might also be a bit biased because I basically teach Calc II now, of course.

 

[S_Happens]

I'll never understand that mindset. To me, Calc II was just a matter of figuring out a systematic method for evaluating integrals and series convergence (the two topics most people seemed to have the biggest issue with, at which point 95 percent of the problems became pretty straightforward. Calc III actually required us to understand the math at a higher, more conceptual level and demanded a lot more proof. Plus, I always thought that the multiple integrals and vector calculus sections were just tricky.

I might also be a bit biased because I basically teach Calc II now, of course.

I can only speak from my own experience. It's not surprising that different people will have differing experiences and difficulties in different areas of a subject. It could have to do with the student, teacher, or many other things. I had a wonderful teacher/lenient tester with a class of 5 people for calc 3, while my calc 2 was taught by a thick accented foreigner, 80-100 students, and horrendous exams. When I say lenient vs horrendous exams, I'm comparing the difficulty of the exam vs homework/quizzes/class material.