I am about to start Calc 3 next week and I was wondering if its different or very similar to Calc 2. Which topics from Calc 2 should I review the most? Which course (calc 2 or 3) is easier, in your opinion? Thanks!
Calculus 2 vs Calculus 3
Page 1 of 17 Replies  4258 Views  Last Post: 16 September 2013  01:51 AM
Replies To: Calculus 2 vs Calculus 3
#2
Re: Calculus 2 vs Calculus 3
Posted 20 August 2013  07:56 PM
Moved to Student Campus.
Calc 2 is mostly singlevariable stuff. Calc 3 is multivariable. In a traditional class, you'll get partial derivatives and gradient vectors; multiple integrals; and lastly curl and divergence, with Stokes', Green's, and the Divergence Theorems. It's generally a rush at the end to finish the last three. Calc 3 generally starts out easy, so don't get lulled into thinking you're good. It gets tougher at the end.
The Calc 3 course I took ended with Series and Sequences rather than curl, divergence, and the three theorems I mentioned. Some schools split multivariable calculus into two classes. The second of the split courses is generally more mathematically rigorous and spends more time rather than rushing through curl, divergence, etc. You also get some review of earlier concepts.
Honestly, as long as you can integrate, that's about as much preparation from Calc 2 as will help for Calc 3 (imo). Being visual is nice too. I had trouble with multiple integrals since I'm not a visual person. I had to figure out how to handle multiple integrals analytically rather than by using shadow curves. I also didn't get level curves until I took my Microeconomic Theory course, where we used them with indifference curves. Again I'm not a visual person, so Multi wasn't my favorite class.
Calc 2 is mostly singlevariable stuff. Calc 3 is multivariable. In a traditional class, you'll get partial derivatives and gradient vectors; multiple integrals; and lastly curl and divergence, with Stokes', Green's, and the Divergence Theorems. It's generally a rush at the end to finish the last three. Calc 3 generally starts out easy, so don't get lulled into thinking you're good. It gets tougher at the end.
The Calc 3 course I took ended with Series and Sequences rather than curl, divergence, and the three theorems I mentioned. Some schools split multivariable calculus into two classes. The second of the split courses is generally more mathematically rigorous and spends more time rather than rushing through curl, divergence, etc. You also get some review of earlier concepts.
Honestly, as long as you can integrate, that's about as much preparation from Calc 2 as will help for Calc 3 (imo). Being visual is nice too. I had trouble with multiple integrals since I'm not a visual person. I had to figure out how to handle multiple integrals analytically rather than by using shadow curves. I also didn't get level curves until I took my Microeconomic Theory course, where we used them with indifference curves. Again I'm not a visual person, so Multi wasn't my favorite class.
#3
Re: Calculus 2 vs Calculus 3
Posted 20 August 2013  08:40 PM
#4
Re: Calculus 2 vs Calculus 3
Posted 20 August 2013  08:50 PM
If it's a traditional Calc 3 class (meaning it isn't split into two classes), then yes. You get line and contour integrals at the end with curl and divergence.
If it is a twoclass sequence, then integration is about 1/3 of the class.
Double integrals fall under multiple integrals. They show you how to deal with double and triple integrals. You can expand that out to higher dimensions, if necessary.
If it is a twoclass sequence, then integration is about 1/3 of the class.
Double integrals fall under multiple integrals. They show you how to deal with double and triple integrals. You can expand that out to higher dimensions, if necessary.
#5
Re: Calculus 2 vs Calculus 3
Posted 01 September 2013  04:17 AM
The concept of double integrals isn't 'hard', you just integrate once, and then integrate the result.
In Calc III you have to do a lot more problem formulation, making the equation into something you can work with, by using identities, or changing coordinate systems, from Cartesian to Polar, for example, as well as working with projections of curves onto surfaces.
It's all quite doable but you need to work a lot of problems to nail each concept. If you plan on taking any other Calculus courses, keep good notes, you'll use this stuff a lot. I hit PDE's in my next semester and I wish I'd spent more time working problems in Calc III I can tell you!
In Calc III you have to do a lot more problem formulation, making the equation into something you can work with, by using identities, or changing coordinate systems, from Cartesian to Polar, for example, as well as working with projections of curves onto surfaces.
It's all quite doable but you need to work a lot of problems to nail each concept. If you plan on taking any other Calculus courses, keep good notes, you'll use this stuff a lot. I hit PDE's in my next semester and I wish I'd spent more time working problems in Calc III I can tell you!
#6
Re: Calculus 2 vs Calculus 3
Posted 03 September 2013  01:55 PM
Also study your trig. Think Calculus 3 is easier. If you've been able to reach up to that level then you have already been dealing with the main concepts of calculus (differentiation and integration) for sometime. Its basically the same, but a higher level. You start to study the concepts at the third dimension.
#7
Re: Calculus 2 vs Calculus 3
Posted 04 September 2013  10:59 AM
streek405, on 20 August 2013  07:47 PM, said:
I am about to start Calc 3 next week and I was wondering if its different or very similar to Calc 2. Which topics from Calc 2 should I review the most? Which course (calc 2 or 3) is easier, in your opinion? Thanks!
Personally, I think that Calc 3 is way more rigorous and definitely requires more understanding of abstract concepts and generalizations than calc 1 or calc 2 do. If you are already familiar with and understand concepts from your previous calc, you should be fine...I just wasn't used to having to study quite as much as I had to for 3.
It is very interesting though, and doesn't introduce many more calculus operations...rather it expands on them, teaches different uses and manipulations of them, and of course introduces them with a third (z) variable.
Just spend a lot of time with your textbook and do lots of practice and you should be fine!!
#8
Re: Calculus 2 vs Calculus 3
Posted 16 September 2013  01:51 AM
I had a tough time with Calc 3's 3D dimensions and all. Zspaces and what not .=
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