# The ever so dreaded Calculus II

Yes, that's right, I said it.

Most of the grad students, professionals, and upperclassmen are probably laughing at my title, either because they breezed through the course, or because they too, remember being a first semester freshman in engineering, and hearing such horrible things about what is coming next semester.

Now I understand that in my major(ChemE), there will be many more demanding courses than calc II, but it seems that many students are either "weeded" out by this course, or simply manage to survive by a dangling thread.

What was your experience with Calc II. I know everyone is different, so I think it is healthy to hear how everyone fared.

a) how easy it was or,
b) explaining how they didn't need to take the course because of (insert reason in order to brag and in the process completely fail to answer the OP).

If it was easy, tell me why. If it was difficult tell me why. From the sounds of things, it isn't the material as much as it is the amount of material, and that is what tends to scare students away.

I think Vector Calc (usually "Calc 3" at a lot of schools) was so much more difficult and I'm only now really beginning to understand a lot of the theorems and concepts.

However some people do have problems with integration. Integration isn't a trivial thing to learn, some people pick it up faster (probably because they've seen it before). I think the trickiest part about Calc II is remembering all the different integration techniques. So pay extra attention and make sure you go to office hours if you are confused once they start doing various trig substitutions, integration by parts, partial fractions.

Good luck! It should not be too hard given a consistent and honest effort.

It isn't the material is extremely difficult, it's that there are a lot of different things that Calc II needs to do, such as methods of integration, series, and parametric equations. Methods of integration and the information about series is pretty straightforward, but it the work can be tedious. The ability to make so many errors on one problem is what, in my opinion, makes the class difficult, although the subject matter isn't very difficult.

Just take your time solving the problems and checking for errors you should do fine.

I think the perception of calc 2 being so difficult comes from the fact that a lot of students are actually surprisingly well prepared for calc 1. It's relatively difficult (compared to calc 2) to think of "real world application" questions that very specifically depend on calc 2 concepts, and so I think a lot of students just find it very difficult to relate to the material. Add to that the fact that there's only a few simple rules that you need to actually memorize to do calculus, and those are what calc 1 is about. Calc 2 is more about building a toolkit, and learning when to use each tool. An easy test can quickly turn into an impossible one when you start hacking away at a nasty-looking integral that really only demanded a simple (but subtle) trig substitution.

Calc II (or calculus in general) can be way more sadistic than it should be. I remember not being very fond of some integration techniques such as trigonometric substitutions or "Rotate around x-axis to find the volume" type of questions because some of the questions can be very tricky and/or tedious. I did enjoy sequence and series, though.

Yeah, its pretty much the quantity of the material that makes it 'hard' though I use the term loosley. I don't know why you're scared of calc II when there are many other courses you should be afraid of. Unless you did bad in calc I, calc II shouldn't give your problems.

A reason calc II is a step up is because the material is all new (integral techniques, series, integration application) whereas most of calc I is done in highschool. Also, calc II uses trig a lot so you won't be able to slide by as you might have in calc I. Some integrals can also get very invovled, and take up a page or two.

I found Calc II difficult because I found it dreadfully boring. Most boring course I've taken to date. "Here's the formula-- don't bother where we got it from, but here's a pretty picture to confuse you-- here's two simple examples to illustrate the tecnhique, and here's fifty million other things you need to know". Not my cup of tea thanks.

I think most people's difficulty with Calculus II stems from problems in Pre-Calculus, and Calculus I. From Pre-Calculus, you really need a fluent understanding of modeling with the basic functions. You should be able to look at different graphs of data/phenomena and generate a reasonable equation without pulling out a reference. You should also have a solid understanding of limits before hitting Calculus I. Being able to quickly shift from words, to data tables, to graphs, to functions should be second nature. If you ask someone "What is Sin(5π/6)" and they don't know the answer through a dynamic understanding of the unit circle, they should probably spend some more time on Pre-Calculus. Likewise, if you can't manipulate an expression with multiple powers/fractional roots or "complete the square", you need some more time with Algebra/Pre-Calculus.

In Calculus I you really need to understand the derivative, and be able to recognize/express it in words, from a table, from a graph, and in function form. Then of course you need to learn the tool box of differentiation techniques. As you do this, you should be able to begin recognizing what integration is all about on a conceptual level. Then optimization and related-rates problems should become fairly easy.

If you have this proper foundation, Calculus II will be a walk in the park through the first 50-75% of the class. You should be able to do u-substitution in your head when learning your integration tools (some people develop the fundamentals of this technique in Calculus I). If you can't do them in your head, do enough problems until you can - some people can do it right off the bat, and some people need a few hundred problems. The applied problems such as computing areas/volumes (of symmetric rotational objects), physics applications, economics, and probability/statistics should come quickly if your foundation is sound. I found the only challenging part of Calculus II was towards the end when we covered sequences, series, and convergence. It took some effort for me to learn all the tests of convergence. Similarly, Taylor and Fourier series problems were often challenging.

So far in Multivariate (Calculus III), I've found the topics to be fairly easy. Having/Developing the ability to visualize in 3+ dimensions is key. We'll see how things progress...

By the way, these are the two texts I used (am using).
Functions Modeling Change is for Pre-Calculus.
The Calculus text covers Calculus I, II, and III (Multivariable).
Great writing/explanations, examples, pictures/graphs, and exercises.

http://www.textbooksrus.com/book_pics_large/0471793027.jpg [Broken]http://www.textbooksrus.com/book_pics_large/047147245X.jpg [Broken]

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Calculus II i thought was more difficult , cause i was bad at series, lol. I got a B in the end, so it wasnt to bad. But, it is demanding

Calc II was the most difficult class I have ever taken. It is so difficult that it has the highest fail rate of any other course required for engineering (around 85%ish). I have never known anyone to pass the class the first time around unless they took it with a very easy professor.

The most difficult part for me was all of the proofs and derivations, as I am not an abstract thinker. Secondly, a ridiculous amount of material is covered in the class. Typically we were moving at about a chapter a week and had a regular lecture 5 days a week with an SI lecture immediately after and student tutoring was available 3 nights a week. While the class was only 4 credits, it easily occupied 8 hours of every day of that semester.

Calc III (multivariable) was a breeze, I rarely studied and did well on every exam in that class. Greens theorem, stokes theorem, divergence theorem, all a pretty easy after calc II.

By the way, these are the two texts I used (am using).
Functions Modeling Change is for Pre-Calculus.
The Calculus text covers Calculus I, II, and III (Multivariable).
Great writing/explanations, examples, pictures/graphs, and exercises.

http://www.textbooksrus.com/book_pics_large/0471793027.jpg [Broken]http://www.textbooksrus.com/book_pics_large/047147245X.jpg [Broken]
[/URL]

My goodness, no wonder you're having trouble on the subject...the one on the right, that is like the worst Calculus book ever! Maybe not to very worst but definitely give it a 4 out of 10 honestly speaking.

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I don't think you read properly. I've already passed Calculus II (with an A).
I really enjoyed that text, and still use it. Many of the criticisms of this text are that it doesn't support proper learning for students who are not "bright" or do not remember trig or function modeling. Well... if a person doesn't know their trig or how to model with functions they should be in a Pre-Calculus class and not Calculus I/II. It shuns the use of MATLAB/Mathematica, and encourages thought and topic interconnectivity with it's exercises and end of chapter projects.

EDIT: I'd like to add that when I said "easy" in my above posts, I did not mean to imply that I did nothing and passed. I showed up to every lecture (three 1.5 hour classes per week), did at least 2-3 hours of reading/exercises per hour of lecture, and continuously reviewed material. By "easy", I mean that things went smoothly with very few topics or questions that I had difficulty understanding.

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Calculus II is considered "difficult" because a few of the key convergence theories arent true for their converse. Some people really dont understand that or get it before the exam, so they end up bombing the class.

In retrospect, I would rather take calculus II than multi variable calculus. I spent a lot more time learning the material in multi variable (mainly because it was abstract and that my instructor/TA was not exactly the best teacher). I remember spending about 8 hours on the theoretical homework (expanding proofs for example) every week for calculus 3. But then again, I did have a theoretical junkie as my instructor.

I ended up getting an A in both classes. My calc 3 class had a 25% curve in it. Where as my calc 2 class only had about a 5 or 6% curve both with respect to get a C.

I took calc II and calc III at the same time. Even without calc II knowledge, Calc III felt much easier and definitely more intuitive for me.

It may have been a difference in professors (loved calc III teacher), but I can say 100% that I spent much more time working on Calc II and received a lower grade.

My biggest problem with Calc II was my professor's policy of "no partial credit." No matter how well I knew the material, no matter how firm my grasp of the concepts, there was very little hope that I could make it through 90% of the exam without a single "silly" mathematical error or sign error.
Mistaking a positive for a negative sign on a 15 point, page long partial fractions question was an automatic 15 points off....already in "B" land.

I really loved the series part, but the diff. eq was not up my alley, so instead of learning all the formulas I taught myself laplace transforms for the initial value problems. I remember waking up 25 minutes late for my diff eq. test, running into the class, sweating, my nose bleeding, no calculator, amazingly enough I still made a 96.
Overall, I thought it was pretty easy; whenever I got overwhelmed by techniques of integration, I reminded myself of the fact that we only learned about 5-6 of them. It also depends on who your teacher is, of course, being me, I got a teacher whose class distribution ended up being 45% F's.

I'm in Calc II now and I have to say, Calc 1 was a joke compared to this..

I'm spending twice the amount of time on the "amount of material" compared to Calc 1...

Your Alg/Trig has to be perfect and you'll get a new concept about every 3 days, the class goes fast and if you ever fall behind you'll be in trouble.

apparently this is the hump in the middle as most people say Calc III is much easier (less time demanding anyway)..

fluidistic
Gold Member
I passed Calculus II last semester. That was the course I liked the most in the first year (maybe along with Physics I but I didn't pass the final exam of Physics I yet). I really loved almost everything I learned with Calculus II. In fact here it's called "Mathematical Analysis II" which probably is Calculus II. But I had to know how to demonstrate all the theorems we were using, that is about 40 theorems/propositions and stuff like that. Appart this, I had to know how to do the exercices. I studied this matter (and only this one) for a whole month during holidays after having took the course. I got an 8/10.
So for me it was difficult (especially due to the fact that I had to remember how to demonstrate so much things) but as I had studied enough, I wasn't scared by the final exam. And yes : I loved this course!

Your Alg/Trig has to be perfect and you'll get a new concept about every 3 days, the class goes fast and if you ever fall behind you'll be in trouble.

apparently this is the hump in the middle as most people say Calc III is much easier (less time demanding anyway)..

Agreed. I returned to physics and math as "post-graduate/non-degree." Because of this, I didn't have to prove my pre-requisites.

Well...I had never taken Calc I, or Trig,....or Algebra. My last class was pre-algebra in 10th grade.

I wanted a challenge, and Calc II gave it to me. lol

in order of difficulty (from hardest to easiest) I would rate it:

calc 1 harder than calc 2 harder than calc3

I've only gotten into my 4 or so week of calc 3 though so we'll see.

integration in calc2 was pretty easy to me, the confusing things were the chapters on volumes and series.

what really helped me in calc2 was to learn from sources other than my book and my professor sometimes, as especially the book made the conceps more difficult than they appeard, these 2 sites really cleared things up and made them simpler for me:

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

http://www.karlscalculus.org/ [Broken]

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