Study Aid Review: Extra Practice with Integrals Volume 2

 

This material covers what is for many people the hardest part of Calc II. Specifically, this set covers the area and volume integration problems and integration by parts. Jason does several problems on the disk, shell, and washer methods for calculating volume, and tons of integration by parts problems. There are a couple other topics that he covers, but those are the big ones. The two things I wish he would have shown in this set were the table method for integration by parts that make the problems much quicker and easier, and showing some of the washer, shell, and disk method problems revolving around an alternate axis. Even without those, he explains the concept far better than the book ever does.

There are a couple caveats I want to make. There are several integration techniques that you will get exposed to in class that are not on this or volume 1 of this set. They are however covered on his calculus 1 & 2 tutor and advanced calculus 2 tutor DVDs. This is really just fleshing out what was on those sets and adding concepts that he could not put into those DVDs. Also while he does a large selection of problems, he does not generally pick the hardest ones to do. He picks the kind that are most likely to show up on a quiz or exam, but not always the really hard ones you get for homework.

 I very much believe in Jason's products and his teaching style. If you use this set correctly, meaning as supplements but not substitutes for class and homework, it will help reinforce the material, shore up lectures that you may not have understood, or serve as test preparation. I made it through the entire calculus sequence at my school with straight A's and while I did have to study hard, these definitely gave me a leg up. I had confidence in the fact that I knew the material and expected to get perfect scores on my exams not just pass them. While that did not happen all the time, it did happen more than once. I was a horrible math student when I was young, and now because of Jason's DVDs and hard work, I am a very good math student and even tutor it myself.

Study Aid Review: Calculus 1: Extra Practice with Integrals Volume 1

 

Anyone who has taken calculus can tell you that doing integration is the hardest part of the first-year calc sequence. And, if you do not get the concept early it will carry over into all the other courses where you need to be able to do integrals. The farther along you get, the more you are going to be expected to do them quickly.

This set really enforces the basic integration techniques. It starts out by introducing the concepts and the use of rectangles to approximate the area under the curve. Jason does not spend time on things like Simpson's Rule, Euler's Method, and the Midpoint Rule, which you will use in class when you first start learning integrals. So, as I have stated in other reviews of Jason's products do NOT rely on this as a substitute for class and homework. It is a supplement for a reason.

The big concepts Jason touches on in this volume are integrating polynomials, exponential, logarithms, and trig functions. Then he spends a ton of time on integration by substitution. It is the most used integration technique (at least the one that can be done without a computer the easiest) and when you learn how to do it fast, it will save your bacon on a lot of exams. In my differential equations final I was stuck on a problem where I could not figure out how to proceed, then I saw the substitution that I needed to make and was able to finish it off quickly.

The better you get at this material the easier things will be in your advanced math, physics, and engineering classes. Jason gives you lots of examples after introducing the topic and goes step-by-step through how to solve them. That process really helps sharpen your algebra skills as well, because many times the calculus part of the problem is very easy, but the simplifying (which is all algebra) is what takes the longest and offers the most opportunities for mistakes.

If your learning style is conducive to watching recorded lectures, Jason's DVDs are the best non-required investment you can make. I have almost all of his material, and it has helped me as a non-traditional student who was horrible at math when I was younger get straight A's in math. I highly recommend his DVDs.

Study Aid Review: Schaum's Outline of Advanced Mathematics for Engineers and Scientists

 

This is not really a book that is tied to any one specific course like the other Schaum's outlines are. This is meant to be more like a reference where you can go to look up concepts that you may have forgotten. It is like a condensed textbook that has the key things that you need to know but does not go into a lot of detail about the theory and do a bunch of proofs as a textbook will. Let's face it, we all forget things from class after a while, especially things that we do not use on a regular basis. Most people will be able to remember how to take simple derivatives or integrals, but far fewer people are going to remember how to set up a triple integral or do Laplace Transforms off the top of their heads after they get done with the classes where they have to use them. That is where this will come in handy.

I think the best way to use any of the Schaum's outlines is to use them in conjunction with learning the concepts in class (because they give you far more examples worked out than your book ever will) or as a reference guide once a class is over. At that point, you can use it as a substitute for your textbook because you will not be as likely to need all the detail and rigor of a full-blown textbook by then. It is not something that is going to be useful to teach yourself the concepts from initially. That is because of the lack of detail and the fact that some of the outlines are edited badly and can contain errors. Once you understand the material the errors and typos can be easy to spot, but when you are first learning that is not always the case. I have only glanced through this particular outline so far, so I am not sure how many errors (if any) are in this one. I know some of the outlines have more errors than others, but just be aware if something does not look right when you are working through a problem, it may not be that you don't know what you are doing.

Study Aid Review: How to Ace the Rest of Calculus

 

The textbook I had for multivariable calculus was absolutely worthless, so I really leaned on this, Khan Academy, Patrick JMT on YouTube, and the Mathtutor DVDs for Calculus 3 to help figure out how to do the problems. 

Unlike some of the book supplements out there, this one does not cover everything you will see in class. The book hits the most important topics and gives several examples, tells you what to look out for, and what some common mistakes are. If you are in Calculus 2, this is not really going to help much. It is almost exclusively things you are going to see in multivariable calculus like double and triple integrals, partial derivatives, Green's Theorem, and the like. You will get some of the sequence and series material you will get at the very end of Calculus 2, but it does not go into all the integration techniques you will learn in Calculus 2. So, if you are in the first or second semester of Calculus, you want what is essentially Volume 1 just titled How to Ace Calculus.

Study Aid Review: The Calculus 1 & 2 Tutor - 2 DVD Set - 8 Hour Course

 

I want to start out with a caveat for anyone thinking of getting this or subscribing to Jason's site. If you are going to be taking Calc 1 and 2 at the college level, you would be best served to get both this DVD and the Advanced Calculus 2 DVD because, depending on your school, what is covered may not be in the same order as what Jason has laid out. Of course, if you subscribe to the site you will get all of the lessons and much more content than what was originally included on the DVDs.

This DVD basically covers derivatives and integrals. It goes very in-depth into both those topics and covers all the main differentiation and integration rules you need to know. Again you need to keep in mind that this is a supplement and does not cover everything you will see in class. I can only use my class as a reference, but we started with a review of functions, then went into limits, then derivatives, and will finish with an introduction to integration. There are also a couple of the topics covered on the Advanced Calc DVD set that will be covered in my Calc I class, which is why I am using that DVD set along with this one. Plus I plan on continuing on to Calc II, so I will eventually end up using both.

The one big topic from first-semester calculus that Jason does not go into much is the topic of limits. He explicitly says at the beginning of the video that is he not covering everything and explains why he excludes most of the material on limits in this set. He has, however, subsequently added a limits tutor, that will cover the material that was missing from this DVD, which is helpful because limits are covered extensively at the beginning of the semester before you get into the differentiation rules.  If you try to study just from this, skip class, and do not do the problems in the book, the first test or two will be a disaster. So don't fall into that trap. And while Jason does not cover most of the limit concepts that you will have to go through in class, I found knowing the material on the DVD ahead of time helpful to understand the "big picture" limit concepts even though I did not know the mechanical process for taking limits ahead of time. He also does not cover all the types of applied problems (word problems)that you will see in class.

Ultimately whether you find this DVD useful will depend in large part on how you learn. This is basically like watching a lecture on TV. Obviously, you cannot interact with Jason as you can with a tutor, and you are limited to the problems that he works out. Some of his problems will match what you get in class, while others may not. I look at these DVDs as showing the basics and presume I will encounter more complicated problems in the book and on the exams. I use them before class to get an idea of what is going on, then from time to time during the semester if there is a concept I did not get completely in class from my teacher, or if I need to brush up on something. If used in that way, and if your learning style is conducive to that kind of presentation, this will be a great investment.

As I said above I strongly recommend that you get this and the advanced calculus tutor dvd if you are taking classes at the college level. There are things in that DVD set like the L'Hospital's rule and inverse trig functions that you will likely go over in first-semester calculus that you will not get on this DVD. The section on L'Hospital's rule will also give some insight into limits. The other concept that Jason does not go into much at all on this DVD is the "technical" process for taking integrals. He does explain it very briefly, but he does not go into detail about how to use the sum of areas of approximating rectangles to calculate the integral. In my class we only got through the first chapter on integration, the first three sections of which deals with that concept. Then we got to the fundamental theorem of calculus, (the second part of which is what Jason does many examples of), and integration by substitution which is also covered in depth here. Many of the sections on integration that are on this DVD will be covered in second-semester calculus (calculus II) at the college level.

In all, this DVD covers about 80% of what you can expect to see on the final for the first semester of college-level calculus. There are definitely things not presented on the DVD that will be covered in class, so again use this as a supplement, not a replacement for going to class and doing homework problems. This is the material that if you can master it you will do well in the class. Mastering this material will also help you understand the concepts that will be covered in class that are not presented here.