Rwecommendations to support for second semester calculus?

[1stepatatime]

Hello everyone, I just finished my first semester of Calculus (first 5 Chapters of James Stewart's "Calculus" 6th edition text) and was able to get some insight from students who were taking Calculus II (the rest of the text).

I finished with an A for Calc I, but heard Calc II is a whole different beast. I enjoy reading the texts to learn, but I also love to have outside sources/references/supplements to aid myself just in case I might get confused. Right off the bat though for summer vacation I will be reviewing my Calc I material (integrals and derivatives) to have as much a solid foundation as possible. I will also try and preview some of the materials in the Stewart text for next semester as well.

My question is, what are some good guides/books/references I can use for my upcoming Calc II class? I was recommended "How to Ace the Rest of Calculus" by Colin Adams by one individual, are there any others I should take note of? Any help would be greatly appreciated.

*Sorry for the mangled thread title btw, I honestly did not realize it was that bad. If I could edit it, I would .

 

[symbolipoint]

1stepatatime, you have started on the correct idea. Review your Calculus 1 material so you will know it better, since you still need it for Calculus 2. Use a syllabus for Calculus 2 to pick the first two-to-three weeks worth of material of Calculus 2 and study this stuff from your current book until the Fall term begins. You could use almost any good undergraduate Calculus book as a supplementary textbook; buy a used one. If you spend more than $2 for one, you have over-spent.

 

[Vanadium 50]

My experience is that most students who think they have trouble with calculus actually have trouble with analytic geometry and/or trig. I would focus on making sure you have this absolutely down cold, and then the calc itself will come.

 

[mathwonk]

what is calc II? several vbl calc? if so, then i agree with getting the analytic geometry well.several variable calc is about approximating the graph of a function of two variables, which is a surface in three space, locally by simpler surfaces, namely planes and quadric surfaces.

so you need to understand the graphs of function like z = ax + by, and

z = ax^2 + b y^2, and how to reduce more complicated quadrics to one of these.or is it integral calc? if so, again it helps to know some geometry of spheres and pyramids.

(you said you studied derivatives and integrals but my sense of stewart's book is that the first 5 chapters do not exhaust the one vbl stuff?)

 

[Howers]

what is calc II? several vbl calc? if so, then i agree with getting the analytic geometry well.


several variable calc is about approximating the graph of a function of two variables, which is a surface in three space, locally by simpler surfaces, namely planes and quadric surfaces.

so you need to understand the graphs of function like z = ax + by, and

z = ax^2 + b y^2, and how to reduce more complicated quadrics to one of these.

Calc II usually means the second half of single variable calc. So he'll be doing things like integration techniques, taylor polynomials, and infinite series. Also, check your PM for a related note =)

OP, you should really know your trig before taking calc II. Review everything you ever learned about sequences and series. Lastly make sure you know how to graph, or rather sketch functions. You will need this skill when finding areas between curves. I believe Stewarts appendix has a good trig section. It has sigma notation too. Just look for non-infinite sequences and series in the text. I also think Stewart has a binomial theorem, so it would be good to get aquainted with the binomial theorem before hand.

Most people suffer because they don't know trig in depth.

 

[will.c]

Stewart is a pretty good text in my opinion. I remember my peers thinking calculus II was a whole different beast from calc I, but I think that's because most of them had a whole year of calculus in a smaller class setting in high school. I don't think much changes except the pace. You seem to already have a good work ethic, and that's all calc II takes. Read ahead in Stewart, and know your trig!

 

[bobattopsail]

I'm taking Calc II this Fall, also using Stewarts. My Calc I ended with chapter 6 and will pick up with 7 and end with chap 11 for Calc II..

chap 7 - techniques of Integration
chap 8 - further applications of integration
chap 9 - differential equations
chap 10 - parametric equations and polar coordinates
chap 11 - Infinite Sequences and Series

I used the "How to ace Calculus" book and it was pretty good as a quick overview of the course. It definitely doesn't go into detail, but a nice preview to get you started, so I can imagine the "How to ace the rest of Calculus" will follow the same thing. I'll probably pick this up soon (used on amazon for < $10) and go over it before I dig into the new material in stewarts. The last half of the book is geared toward Calc III though, which I'll be taking next spring.

For practise there is another cheap book "The Humongous Book of Calculus Problems" that has 1,000 problems with detailed answers covering calc I & II if you wanted to spend the extra time..

From what I've heard, Calc II relies more on Trig / Pythagoras identities even more so than Calc I, so make sure you know that stuff really well... There's also a lot of free stuff out there, like on the ocw.mit.edu website.. Good Luck.

 

[Cvan]

Paul's notes are amazing for a side-by-side calculus reference when learning out of Stewart's. Helped me to have things worded a little differently and get another perspective for calc II. Not that Stewart's is bad--it's an exceptional text for starting calc, it just helps to have some more examples worked through, etc.

http://tutorial.math.lamar.edu/

 

[Dr Transport]

Schaum's, Schaum's, Schaum's, need I say anything more...

 

[1stepatatime]

Thank you for the support/advice everyone, it means a lot to me. The responses have been great especially since so many are in agreement with what foundation should be set (trig/analytic geometry/series). I just started mapping out a schedule of what I will have to work on from now until the fall semester starts.

Today I purchased a copy of Schaum's Outlines for Beginning Calculus (basically what we went over this semester) and "Quick Calculus: A Self-Teaching Guide" by Daniel Kleppner which I plan to work through and expose weak points I know I need to practice. "The Humongous Book of Calculus Problems" also looks like a good supplement to go along with my current method of practice, thanks for the recommendation! I was also looking to get a previous edition of Ron Larson's Calculus text which I found on amazon.com.

Once again, thank you everyone for the replies it looks as though I'll add the analytic geometry /trig/series/binomial theorem to my studies immediately.