What's next in Calculus 2 after a successful semester of Calc 1?

[imull]

So...What's Calculus 2 like?

So I just completed Calculus 1 with an A+ for the semester. What should I be expecting in Calculus 2 if the topics in Calc 1 were limits, differentiation, applications of differentiation, some integration, natural logs, logs, e, and hyperbolic functions?

 

[contrivance]

If you got an A+ in Calc I, you should have no problem with II. Just finished Calc II with an A, and was mostly about all the different types of Integration, and Infinite Series. Smaller topics where DiffEq, Volume of Solids of Revolution.

Opinions of others at my school were that Calc II was the most difficult. some said Integration was hard and Infinite Series was easy, while others thought Integration was easy and Infinite Series was hard.

Personally I found Integration to be the most challenging, although it was a very fun and manageable challenge!

Example, Integration by Trigonometric Substitution was difficult, but very fun when you got the hang of it. (Calc II for Dummies helped tremendously for these topics).

Just study, find the procedure for each method and practice!

 

[imull]

When you say integration, is there much of a difference between Calc 1 integration and Calc 2 integration?

 

[jbrussell93]

When you say integration, is there much of a difference between Calc 1 integration and Calc 2 integration?

The idea of integration is the same but you learn to integrate more complicated functions in calc II. There are basically different integration techniques for different classes of functions. The goal is to be able to look at any function and know which integration technique to use. It is more challenging than calc I but way more fun.

By the way, calc III was my personal favorite (and the most difficult) :)

 

[Nick O]

The more advanced integration techniques in Calc. II weren't so bad, but the infinite series portion was a bit of a hassle. All in all, it's nothing to worry about if you did well in Calc. I.

 

[MathWarrior]

Calculus 2 is a bit of a mixed bag of classes, when I took it. It started off covering vectors, learning that i=<1,0,0>, j=<0,1,0>, k=<0,0,1> etc., and eventually went on to learn all the various mathematics related to vectors, dot products, cross products etc.

Then it moved into integration that is more advanced and applications of integration, such as finding an arc length, surfaces of revolution, integration by parts, and integration by trigonometric substitution. It also covered integrating in new coordinate systems, such as polar coordinates.

Then it progressed to series and sequence problems, each topic is kind of separate from the others you just learned. The fact you change what you are doing in calculus 2 makes it hard for some people, its like you're always learning something new.

If you want to get a good look at what you might be learning I found this site helpful: http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx .

 

[imull]

Sounds like it's going to be really interesting and a nice challenge.

 

[1MileCrash]

Calculus II for me focused solely on being able to integrate new kinds of functions, knowing when to use whichever method, applying integration to solve physical problems, convergent/divergent series, taylor series.

I think the main challenge people/I have/had with Calc II is knowing which method to apply to an integral. It's the first class I can think of where you have to actually make informed choices on how to solve a problem instead of just following a procedure.

 

[ChiralWaltz]

If you want to get a good look at what you might be learning I found this site helpful: http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx .

Paul's Notes are of excellent quality. They highly resemble the textbook I use.

Adrian Banner (Princeton professor) has really good youtube videos. Don't let the 240p quality trick you, they are full of good information and reflect the Calc II course. It is great having a pause button for math professors.

http://www.youtube.com/watch?v=3aqIAzwxDh0&list=PL7923294C6B4B03EE

 

[sheldonrocks97]

I just finished Calc II and it is REALLY HARD. I got an A in Calc I and I am waiting for my grade. I got a D without a curve so hopefully with a curve I will get a C so I can more on to Calc 3. Just because you got an A+ in Calc I doesn't mean you will fly through Calc 2.

 

[dkotschessaa]

People tend to not like series and sequences and such that often form a large part of calc II. It starts off easy enough, and then you start learning all sorts of ways to test for divergence and such, which tends to get away from people after a bit. It's actually some of the most interesting stuff in Calculus, but it is a lot of information, and goes by very quickly.

This might not apply to you but I'll say it anyway...As with a lot of calculus, it's not so much the calculus itself sometimes as some of the rather hideous algebra that sneaks in as a result. Working with rules of exponents, factorials and such, all showing up in the numerators and denominators of some complicated fractions... You'll want to make sure you're super comfortable with all that.

-Dave K

 

[Metta]

I've earned a B in calc 1 with moderate effort. I've had friends who were taking calc 2 this semester and some of them were in the tutoring center five days a week and were still struggling. I imagine it's more difficult than calc 1 but I don't know how much. I am taking it next semester also. Good luck.

 

[TomServo]

Integration is an art. The integration they start you off on is simple, but some integrals are very tricky, and that can range from trig substitution and integration by parts all the way to Gaussian integrals and...other hard stuff. Long chains of integration by parts are a pain.

 

[imull]

Thank you guys. These are helpful.