The Humongous Book of Calculus Problems (Humongous Books)
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The only way to learn calculus is to do calculus problems. Lots of them!
And that’s what you get in this book–more calculus problems than your worst nightmare—but with a BIG difference. Award-winning calculus teacher W. Michael Kelley has been through the whole book and made a ton of notes, so you get:
• 1,000 problems with comprehensive solutions
• Annotated notes throughout the text, clarifying exactly what’s being asked
• Really detailed answers (no more skipped steps!)
• Extra explanations that make what’s baffling perfectly clear
• Pointers to other problems that show skills you need
And all of the major players are here: limits, continuity, derivatives, integrals, tangent lines, velocity, acceleration, area, volume, infinite series—even the really tough stuff like epsilon-delta proofs and formal Riemann sums.
So dig in to your heart’s content!
53 reviews for The Humongous Book of Calculus Problems (Humongous Books)
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MGSWS –
What a geat book, especially for self study. If you use it along with other problemn collections like the Schaum’s series, you should be able to solve almost any problem in a Calc I or II level course.
thesecondjt –
This book is 10x better than Kelley’s “Idiots Guide to Calculus.” Why is that? He solves more rigorous problems that you are likely to see in your Calculus homework. He completes every problem step-by-step (including the algebra tricks!) so you’ll know how to apply the techniques to problems you are likely to encounter. Highly recommended!!
Kersi Von Zerububbel –
This is a great text for someone just getting into Calculus. The author does assume that one has taken high school Algebra and Geometry. Most of the concepts are introduced via the intuitive method rather than proofs but that is what makes the text very accessible. For the cost this is a bargain. Very good for the beginner and someone who wishes to get back into the subject after a long absence.
Melanie Shirling –
This book is truly written for people who really do not speak math…like myself! I understand what he writes about…and my calculus text is ridiculous to try to understand. This seems to be the perfect compliment to a class. Highly recommended. One thing I do wish is that there was some space between the problem and the solution so that we could try to work the problem out…but then the book would be even bigger and that’s not practical. I guess just keep on with sliding the paper down the page…
Natalie Miller –
I’m going back to school after a long time away. I’d never taken calculus in my first time through undergrad and graduate school so I was nervous about taking it the first time.
This book is handy in that it explains, in pretty simply language, what’s going on in a certain step, especially in those steps were people most often say, “Huh? Where did *that* come from?”
If you’re looking for a book that gives you the same basic problem asked for in many different ways, this isn’t the book. Go for Schaum’s or Problem Solver by REA. But this book might help you figure out exactly what you’re missing if you’re working your way through a million Schaum’s questions and find yourself stuck.
Douglas F. Mitchell –
lots of problems explained: excellent example problems all done out for basic explanations or even a review if you or your parents are a little rusty. Similar excellent review for Humongous Book of Algebra problems
Darcy Pennell –
As with some others who have reviewed this product, it wasn’t what I was expecting. I thought it was going to be a book of practice problems with full solutions. It turns out it is actually a study guide. For each topic there are a handful of worked out examples, but no practice problems. I didn’t really need help understanding concepts, I just wanted to practice the concepts so that they would be firm in my mind.
For someone who is struggling in Calculus and needs extra help this is a good book. The explanations are well-written and detailed. But for someone who is looking for practice problems, this book is not what you are looking for, especially if you already understand the math.
If you need help buy this book, it is very good. If you need practice look elsewhere. I really liked
3000 Solved Problems in Calculus
. For comparison,
3000 Solved Problems in Calculus
has over 60 related rate practice problems, The Humongous Book of Calculus Problems had around four example problems and no practice problems.
M. W. Hill –
After a year long absence between my calculus 1 and calculus 2 classes it was suggested to pick up this book for review. this book is not only giving me a thorough review, but keeps my attention. Overall I think the best part of the book is how when working through the problems the method used and the steps taken to complete the problems differ. Unlike a traditional mat book where a set way is presented and the student then applies the formula 25 times in a row before moving on.
Matilda –
I strongly recommend this book to anyone who is taking Calculus. Each problem is explained step by step and the formulas are constantly reminded. There are a wide range of problems from easy to difficult which makes learning gradual and permanent. The writer has a good sense of humor and is a good teacher.
Saundra –
I am really happy with this book. The review section is great and the layout is very clean. However, I have already found a few mistakes which makes me wonder which mistakes I am missing. Could really use an errata.
Abhinav Jain –
I like this book a lot! it clears up many different things in calc. definitely worth it if you are struggling in calc.
Dancingdaisy –
This book is a great reference for when I am doing my homework on the book required by my calculus course. Whenever I do not know how to approach a certain type of problem, when I am looking for the right steps and rules or even just the algebra behind certain equations, this book helps me out! One of the things that I always have to deal with, is the fact that my math professors are always skipping steps when solving a problem or even when correcting a test; this book will give you everything, step-by-step, and not leave you in the dark – having to spend at least twice the time solving a simple problem just because you got stuck on a silly step. CALC 1 AND CALC 2 here!
J. D. Sebastian –
I just got this book and read through the first three chapters and perused through the rest. I’ll read them thoroughly soon enough. So far this book is OUT-FRACKING-STANDING!!!! Loved reviewing linear equations, inequalities, slopes, functions, etc (and yes, I really did love it). Topics that I’ve long forgotten and haven’t used since college in a College Algebra & Trig course way back in the mid-90’s (yes, I’m old(ish)).
This book is a God send. The explanations are easy to understand and most importantly–YOU GET IT! I needed something to help me with my review and preparation for Calculus and Krantz’s inappropriately titled book “Calculus Demystified” (you can check out my sordid review on that book, later) wasn’t cutting it. Kelley’s book, along with Jason Gibson’s Calculus 1 & 2 DVDs (see mathtutordvd.com) are a great combination, throw in Khan Academy’s free Calculus video tutorials, and you should be rockin’ in paradise, folks.
However, being that the product description led me to believe this to be a workbook of actual Calculus problems, I was a wee bit disappointed not to find any problems to work at the end of the chapters (hence, the four stars). So, Mr. Kelley, how about some problems to work in the next edition? And don’t just give us the answers to the odd numbered problems. Include the answers to ALL the problems.
Bottom line, with or without the problems to work, get this book. It won’t end up in a burn pile like a certain aforementioned book. Where’s Fireman Montag when you need him?
D. Davis –
I am a strong “C” student and struggle with almost every class. I purchased this book in anticipation of my 3 calculus courses and the book made things so much easier. It really works for me; a dumb kid taking a smart kid class:)
gr8one67 –
I found this book to very helpful with both differential and integral calculus classes. the way it explains the subject matter was better for my brain than the actual textbook. plus there are tons of examples to work out that also provide step by step instructions on process.
Wikiteach –
I am studying to take my PRAXIS exam as a non-math major and quickly found out that I needed the proper tools to prepare. I attempted to use PRAXIS ETS books to no avail and thought I should just find subject specific texts that could enhance my knowledge in the core areas of the exam. Well, there are way too many Calculus books out there and no matter how easily learned they say that Calculus can be, none of them were written for the non-math (but very capable) student of the subject. THIS IS THE BOOK FOR YOU. If you want a book that details (step by step) the process of learning, gathering, researching and proving Calculus problesm, it’s THIS BOOK.
Finally, a book that stays true to its title and we’ll know more when I finally pass the PRAXIS.
Wish me luck!
tony –
It not only provides us math examples, but only gives us many formulas. The writer leads us to where we need to start and how to practice math easily. I prefer to learn math this way, so I feel painless to math any more. Very helpful. Worth money.
William L. –
I purchased this book in hopes that it would prepare me for going into Calculus 2 during my next year in school. I thought that this book only covered Calculus 1 topics, but it actually goes over the basics of Algebra/Pre-Calc material, then Calculus topics, and then even Calculus 2 topics. I am more than pleasantly surprised, and the way that the problems are presented is excellent. The answers so far have been complete and very knowledgeable. There are explanations in this book that clear up topics from algebra that I never did fully understand.
If you get this book in hopes of preparing for a Calculus or Calculus 2 course, then I would recommend studying around a chapter a day. There seems to be about 8 chapters of Pre-Calculus/Trigonometry, then around 16 chapters of Calculus 1 Material, and finally 4 bigger chapters of Calculus 2.
So far I’ve been working at a pace of about a chapter a day, and reviewing material that I had trouble with the next day before moving on to the next chapter. So far I’m learning a lot, and I expect to solidify my knowledge of both calculus and calculus 2 over the next month!
Whatifitistoday? –
This is a good book to read prior to taking a calculus class, or in my case, if you are trying to brush up on it because you took calculus in the dark ages and now you have to help your kids with their homework! You must have a solid math background (have the prerequisites for calc) or you will be lost. Good book though and I’d recommend it.
L. Younge –
This book is a good review for differentiation and integration problems. I bought it so that I could brush up on my skills.
d7727272 –
EVER NOTICE YOU READ A CHAPTER IN A MATH BOOK AND END UP NOT UNDER STANDING ANY OF IT!! THIS BOOK TOTALLY FIXES THAT!!!
Basicly what the author did here is wrote everything out in “math language” than right next to it in “normal language.” so every time you read something you understand it! for instance when the problem says “Advanced infinite series” he puts “series that contains X’s” next to it, making it easy to under stand. A GREAT BUY FOR PPL WHO DONT SPEAK MATH
A Big Ten Alumna –
I purchased this book because I wanted to go back to school and major in Mathematics. In hindsight, I think it was not the wisest decision to take Calculus II (in the summer) when it has been over five years since I studied math. Regardless of my premature leap into the class, I have to say that it helped a little bit for the topics we did covered. I feel that this book would be better for Calculus I and first sections of Calc II but this is based on the Calc II I took at a local junior college. I really appreciate that they worked out a couple of the problems so you can see how to solve the problems.
By no means this book is perfect because it doesn’t cover some of the more advanced topics of Calculus and some of the problems that they worked out left me more confused than ever. In all, I think it is a great book to have in your collection and I would recommend referring to online tutorials on YouTube (i.e. Khan’s Academy and countless others), Schaum’s series, and the Calculus Lifesaver book (not the exact title). This is not by any means a substitution to actually paying attention in class, taking good notes, and asking questions if you are unclear about a particular problem. I would highly suggest that you borrow this book from the library before making the leap in purchasing this. I did just that but unfortunately the copied I had in possession had the very pages I needed to understand certain problems. I notified the librarian of the fact.
Miss BG KING –
This is the second copy I have purchased. I sent one to my niece in Washington DC. She found it to be very helpfull. She’s a college freshman.
CEddy470 –
Where this book really shines is as a transition from a lecture to cranking out problems on your own. Often textbooks will give a few “worked” examples, leaving out steps that aren’t directly relevant to the chapter or only showing one way of doing something. Because Calculus incorporates the majority of high school algebra and trigonometry, it is a trial by fire on how well you know that stuff and it’s more than easy to get lost in the algebra. That’s where this book comes in handy – having each step spelled out with pointers to where it incorporates other topics is extremely helpful. If you’re not comfortable with complex fractions the difference quotient is a nightmare. However, because this book starts with an overview of key topics in algebra and trig, you can move into calc without getting tripped up on logarithms or trig identities.
Doing the problems in this book and checking yourself against the answers in this book is the easiest way to learn how to do math. While this does give you a concrete understanding of how to work the problems, you’ll find yourself wanting more problems to test and ingrain the knowledge you’ve acquired. There are about 5 – 15 problems on each topic (about 40ish per chapter). The original reason I decided to pick this up was to bridge the gap between the precalculus materials on Khan Academy and the Calc 1 module on MITopencourseware. The system I’m using is to watch the opencourseware lectures, follow along with the problems in this book, do additional problems in a cheap textbook for more practice, and then use the OCW problem set as review and metric. This is a great supplement, but you need something else for lectures & explanations of what’s going on as well as more practice.
This book takes the fangs out of Calculus and I honestly wish there was a “doorstop” edition of this book with even more problems.
Jordan M –
I’ve been brushing up on my skills for Calc II this upcoming semester. This is exactly what I needed. There’s a lot of review of pre-calc/algebra topics available if you need them.
Brad Jeffries –
The Humongous Book of Calculus Problems is a great book for anyone interested in learning Calculus for the first time or for people who just want to brush up on what they’ve learned. It walks you through the subject step by step leaving no stone unturned. It’s structured so that you’ll continue to build on the preceeding chapters in the subsequent chapters. The author, Michael Kelley, adds sidenotes to the formal definitions at the beginning of each chapter in order to clarify any heavy jargon that would seem superflous to students new to mathematics. Kelley focuses on “the point” of each chapter by explaining why it’s important to know and how it’ll be used later down the road. The only problem I could find in the book was that there were a few minor errors in a few of the problems. However, you didn’t need to be very adept in math to recognize them. Also, there are tons of problems in the book (hence humongous), so I can understand that there might be a couple mistakes in one or two. Overall, the book covers Calculus in great depth by giving you lots of practice at solving Calculus problems while also helping you understand the key core concepts. If you’re wanting to learn Calculus without all the unecessary rigor and monotonous drab of a formal textbook, I’d definitely recommend buying this book.
Erika Chu –
I need help with calculus so bad and when I purchase this book it was my buddy. It has alot of examples that you can look at and you would understand the concept much better. I found this book very helpful especially if you have a professor who does not teach well.
Ann Thomas –
I chose this rating because it is true. I wish that I had this book when I was attending college. I like everything about it that I have covered so far and I would recommend it to my grandchildren and great-grandchildren
Ann M. Thomas
profgeof –
A MUST for kids struggling with calc!!! Lots and lots of good hints in this book. Enjoy – nothing to compare
William Brian Mays –
I am currently in my second semester of Calculus, and I refer to this book constantly to see how a particular type of problem is worked out. The author does each problem step-by-step, not leaving anything out. It’s great for test review as well as just a “second opinion” on how to work a problem you see in class.
Mr. Math Expert –
I own just about every Humongous book in the series, and I like this one: The Humongous Book of Calculus Problems.
It’s been a very long time since I did a lot of work on Calculus, and working with the book took me a year and a half since I was on and off with it. It has been a good journey for me. However much I like the book, I still think it needs a lot of improvement.
As the book claims to have 1,000 Calculus problems, that is not true. The first 8 chapters and the first half of chapters 24 and 26 are worthless as they should have been confined to the other book covering Algebra/Precalculus problems and the space be devoted to Calculus only. I counted them up, and that is 307 problems that are not Calculus. It accounts for 30.7% of the book, almost a third. What a waste.
It’s just weird to see a lot of Conic Section questions in the beginning yet they have pretty much zero presence in the rest of the book. There are some topics missing, and some of the other topics aren’t comprehensive enough as they should’ve been. For example, there is nothing about logistic growth.
Chapter 28, covering the Taylor and Maclaurin series, is weak and redundant. It doesn’t even go in depth about them either. There is not enough coverage of applications. Worse still, the author doesn’t even bother with vector calculus or mixing calculus with linear algebra. I don’t even see much of Calculus word problems related to physics.
As for the rest of the book, it has been very good as the author goes in great lengths in explaining the solutions in details. Sometimes, he doesn’t convey a better technique or makes it simple enough. A point in case is during the coverage of the centroid. I hated what the author gave to the reader, the complicated formula, when there is a much better presentation of it that makes it intuitively easier to memorize.
The readers may think that reading The Humongous Book of Calculus Problems will simplify the language, but it won’t happen. It’s just still the standard Calculus language, and attempting to change the way the language has been conveyed will not solve the dilemma. Either the readers will have to spend a large quantity of time with the material to truly learn the subject or they will be forever locked out. The author has good notes on the sides that put things in perspective.
A few of the reviewers here did not find The Humongous Book of Calculus Problems a useful book for the AP Calculus; I absolutely disagree. This is a very good book that actually explains the major concepts very well and goes through them in a step-by-step manner, tackling the tough ideas during the procedures.
I feel confident that after going through The Humongous Book of Calculus Problems, I have seen my base knowledge of Calculus particularly indurated. I advise the readers to advance to the next level of Calculus which is physics orientated to unleash the power of Calculus.
All in all, I think The Humongous Book of Calculus Problems is a need of an update, to throw out the 307 problems and keep the book strictly Calculus with additional topics and application based problems while making Chapter 28 a better one.
Errata
3.1 of pg. 28 should be a plus sign in the expression
11.32 of pg. 164 should be 56, not 64.
11.39 of pg. 167 should be 7 as the solution (before it says ” ,does”), not ½. Again, in the next two functions, it should be equal to 7, not ½.
11.40 of pg. 167 should be 7 (before it says ” ,does”), not ½.
11.41 of pg. 168 should be 5 , not ½ and 4.
11.42 of pg. 168 should be 1 and 4 respectively , not 0.
14.19 of pg. 215: the whole thing is incorrect. It should be x sub 3 = [(1.75)^2 + 3] / [2(1.75)] = 1.73214. And then, the accuracy will be |sqrt(3) – 1.73214| = 0.000092.
16.8, 16.9, and 16.10 of pg. 252: “a minor axis of length 12,” not “a major axis of length 12.”
22.8 of pg. 397: dx should be included in the integrand after “Calculate the volume of the solid.”
23.10 of pg. 431: [I was mystified about the whole thing until I realized something was obviously missing] Add the pi(r^2) to the formula.
25.18 of pg. 477: the final answer is 9,082, not 9,028.
28.2 of pg. 530: it should be 9, not 8 in the denominator.
seaside mom –
I am teaching AP Calculus AB for the first time, and still struggling to find the ideal text for my students. The Humongous Book of Calculus Problems comes closest. I really love this book, and use it as a reference all the time for my class. It is fantastic for the detailed pre-Calculus coverage, and for the complete, very thorough examples of each Calculus topic. The author starts with fairly simple problems, and gradually builds in complexity in manageable, logical increments. Plus, it’s written in an entertaining manner, and is incredibly inexpensive. Alas, it is not perfect. Sheesh, what more do I want, you ask?
What would make it absolutely perfect would be if: 1) It really was a textbook, that is, if it added now-do-it-yourself exercises for students to practice each concept and 2) It clearly delineated AP Calculus AB vs. BC topics for the teacher who wants to focus on students passing the AP Calculus AB exam. For example, the solids of revolution chapter mixes examples requiring integration by parts with ones that don’t require this technique. Solids of revolution by the disc method is an AB topic; integration by parts is BC and therefore a nicety, not a necessity, for my students.
Still, the best book I’ve found for the clarity of its examples.
JKO –
As a math teacher I recommend any of Kelly’s books to people who have difficulty with math. He makes it easy to understand and shows lots of examples.
J. Hopkins –
I’m one of those guys who was never good at math in high school. I got to college and really bore down hard and started pulling A’s. But I found I love step-by-step instructions that leave nothing out. This is that book for me. I need help with a concept, find it in here, look at the instructions, and then apply the methods the author uses. A really great buy at $13. I’ll let you know how it helps at the end of this Fall semester!
SouleStatistics –
I used this along with several others in this series to review my Calculus for the National Board YA mathematics assessment. It was exactly what I needed. It is not a stand alone book, but great as a supplement or review. It helped me recall my calculus after 20+ years.
adoughe –
Many problems with solutions and annotations help the reader understand the solutions. I recommend this book to any student taking calculus.
D. Welles –
Everything you need from A-Z. If you need a good review or just a little refresher this book can help you. Examine the step by step instructions and take note of the special warning notes. The great thing about math is if you follow the rules and work problems out step by step using the correct methods you canmaster the skills.
Malinda Hawkins –
This was a great book but like the other requires time and a your own scheduled like lesson plan in order to complete the book. It is best done during a break.
heylookhere –
I’ve taken up to Calculus II (Integrals) using this book and it has been very helpful. The explanations are straightforward and nicely laid out so it’s easy to follow. It’s basically a book of problems that are explained step-by-step with no irrational how-did-you-get-there jumps.
There are a multitude of examples for you to follow and work with that cover different aspects of the same material. The book itself ranges from Algebra to beyond Calculus II so it has longevity. I will say that the book does not teach you math. It’s more of a supplement/resource to a textbook or whatever you’re being taught in a classroom. I thought it was well worth the money and it made math seem less daunting.
Jacob Howard –
In learning math we have two different enemies, one is the material, in it’s complexity we struggle to understand the topic. THe other enemy which is far more vindictive is the inadequate instructor. So many math instructors are unacceptably lacking the oratorical skills as well as basic teaching skills to be proficient in math. This book works a lot of problems and writes written explanations to go with them, WHICH IS WHAT YOU’D OBVIOUSLY EXPECT IN A TEXTBOOK BUT NEVER GET. It’s painfully frustrating when you get these PHD holding arrogant charlatans write these textbooks in nonsensical jargon that only a savant like them could understand. BUy this book if you’re taking calc in college and it will help you. For this price, it’s not a dangerous investment, seriously.
Hosun Yoo –
good quality! perfectly works!
Inexpensive and fulfilled satisfaction!
Delivered on time with no damages!
good to recommend!
No worry!
I plan to buy another one when I get chance to…
EC –
Stunningly good book, provided you use it as a post-read to a traditional calculus text, or specific topic within a text. I think this was the intent of the book. The author has a way of focusing in on “This is what they mean” that really helps one understand, and appreciate the more theoretical approach. Lots of practice problems that build confidence, and enhance understanding.
Great book!
Eric
Anita –
Im taking calculus one and this has helped in the way that it breaks everything down and doesnt expect you to know everything that is math.
C. Fritsch –
All of Michael Kelley’s Humongous books are a major addition to the libraries of self-learners like myself. It does require patience, however. To get the most out of this book you need to work all the way through it, not skipping any part. This is particularly true if, like myself, your knowledge of calculus is wide but not very deep. Going through this text rectifies this for me. Most standard calculus texts just give you the answers to every other problem. What if your answer differs from the one in the text and you know your solution methodology was correctly followed? Very often this is not a problem with the calculus part of the question but with the algebra used in final simplification of your answer. Here such difficulties are removed. A top-notch effort that’s very well done. Thank you so much Mr. Kelley.
SHEiK124 –
Try and imagine your Calculus teacher hovering over your shoulder and giving you a play-by-play of how to solve a certain problem. This textbook is chock-ful of example problems for just about everything you could expect to find on the AP Calculus AB and BC exams. It’s a great “study guide”!
D. Page –
After spending 15 minutes with this book, I feel the I’m-going-to-fail-nausea start to dissipate. Really glad I bought this book.
P. enner –
there are lots of great tips in this book. our son likes it very much. thanks so much for this book.
CG –
This book is good as a quick and dirty reference for Calculus problems. It doesn’t have many practice problems but instead each topic has entire sets of problems with different variations that are helpful when you find yourself stumped by a problem and cannot figure out the solution.
Craig Beck –
I have only used it a few times, but found it helpful. Thumbing through it, it seems to be the same quality throughout.
Nikki Bryan –
It seems to show very clear execution and directions of how to do certain problems. I tried to give it 4.5 stars.
Charlotte –
This book gives good, clear, concise information needed to review Calculus. I like how it explains the problems and gives answers in a clear format.
sherelyn nichol –
Got his for my geekie chubby hubby to keep him busy. And that is just what it did. He loves it, but said he does not want anyone to know because they will make fun of him!
Araktsu –
But since then I went through more thorough texts.
I just happen to like focusing my mind on problem solving strategies for this sort of thing.
It is 100% pure math if I remember correctly, not much in the way of applications.
If you have got past algebra, and have a choice between reading this or watching television, read this.
One of them makes you smarter, the other makes you stupid.
You figure out which one is best for you.