The Humongous Book of Calculus Problems

This book is mostly a problems repository. Like the author's other "humongous" books, from chapter 1 it starts giving you problems with very little setup or theory up-front. It does have a chapter introduction page that introduces the topic(s) in the chapter, but then it just starts in with example problems. But, unlike some of the other guides out there that have just a ton of example problems in them, the author does weave in the explanation of the theory in the form of margin notes that are added to explain how to tackle/solve the problems. Along with the theory, the author gives you tips for solving different problem types, advice on things to look out for, and marks the hardest kinds of problems with a skull and cross bones, which I think are good problems to go over before your exams. The book is good in that it does not just dive into the calculus material. The first 8 chapters (about 120 pages or so) are a review of algebra and trigonometry, making sure you have the fundamentals down in case you need to brush up on them, and then it gets into the calculus material. The calculus material covers all of the topics that you will be exposed to in the first year of calculus, starting with limits and ending with using integration techniques on sequences and series problems. It also goes over the introduction to differential equations that students usually get in the second semester, and has good examples for solving related rates problems and optimization problems. The book does not cover multivariable calculus, linear algebra, or the more complicated differential equations material that you will get in later classes if you need to go beyond calculus 1 and 2. This will, however, definitely help you get through the material in the first year of calculus, especially if you have a hard time understanding your textbook and/or your teacher.

The HUMONGOUS BOOK OF CALCULUS PROBLEMS is an awesome book if you're looking for a great explanation or review of Precalculus and Calculus I and Calculus II. Consisting of 565 pages and 28 chapters, topics include: Linear Equations & Inequalities, Polynomials, Rational Expressions, Functions, Logarithmic & Exponential Functions, Conic Sections, Trigonometric Fundamentals (including graphs, identities, and equations), Limits, Continuity, Basic Differentiation Methods, Derivitives (Basic and Advanced Applications and Techniques), Finding Areas, Integration (The Fundamental Theorem, Rational Expressions, Advanced Techniques, Volumes), Parametric and Polar Equations. Also added is a one chapter review of Differential Equations and 3 final chapters dealing with Sequences, Infinite Series, and various tests analyzing them. The author's statement that "Just about every single kind of calculus problem you could run into is in here" is true! But to me, what makes this book really awesome are two things: 1) The author has complete solutions to all 1000 sample problems. 2) He also includes very helpful sidenotes explaining important steps in the solutions. Yes, for a person doing the book as a "Self-Study Review" its a dream come true! I noticed some reviewers have commented there are are no additional problems to try to see if you've grasped the concepts. I can understand their concern, but here is how I worked thru the book: I began each chapter studying the basic concept it dealt with along with the various definitions and side notes. Then I worked each problem in the order they appeared, checking my answer with the author's solution afterwards. Working thru the book this way worked for me. I suppose extra problems (with just the answers) would be nice at the end of each chapter but I was happy with the book as is.

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.

No scribbles on it a little bent but expected for the discount very happy

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.

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.

I have also read an another much better written book by the same author (Humongous Book of Statistics Problems) and I am disappointed by this academician book that is not much better than a standard Calculus textbook. Most of this book is dedicated to theoratical concepts of Calculus. There is, of course, nothing wrong with that. Except that the book is just as dry, boring, and uninspiring as regular Calculus textbooks that most of us would fight to stay awake while reading. There are only few problems dedicated to practical application of Calculus. The rest is dedicated to graphs, limits, theorems, and equations. That's too bad because Calculus is one of the most, if not THE most, practically useful mathematical concept known to man. The book also spends surprsingly few pages on differentiation and integration. The maximum and minimum values using differentiation, for example, are hardly covered and certainly not covered in depth. I don't believe in learning Calculus for the Calculus itself (learning how to draw graphs and finding its limits and areas etc). I want to learn Calculus so I can use its power in real life. In that, this book was quite disappointing.

Awesome book! If you are trying to brush up on some dusty skills or fill in some gaps all of the "Humongous" math books are great. I own all of them. I would caution against using them by themselves if you are searching for a deeper understanding or looking for proof based math. Your best performance will come from a balance of these books, college texts, problem sets and solutions, and a MOOC or some online videos. This book will teach you how to get math done from a calculating perspective but lacks a bit in the development perspective. That is not a weakness though. It is a strength since it puts this as a specialty tool in my library. Because it is a calculating teacher (as opposed to taking a development approach like an intense proof based class would), using this book will free up mental bandwidth you can use to pursue that deeper understanding. In other words, since you will gain a solid foundation and great confidence in basic problem solving you can devote more attention to harder issues that you will deal with in college level mathematics (if that is what you are trying to do).

Great practical book

The book is great for non maths people, the explanations are well intriduced. I recommend this for maths students who are weak in some topics. A+++

I'm using it to prepare for Calc II. Only 20 pages in but so far this book rocks. What I really like about it is that these are GOOD questions because they test your understanding to see if you really understand the material and more importantly, they bring out the little details that are easy to miss. I don't normally write reviews but this book deserves it since it really is something special. Other books just bore you by telling you most of what you already know. You don't master math by having a general/basic idea of concepts, you master it by doing tons and tons of problems and this book seems to be based on that principle. I feel confident that if I can do every problem in this book, I'll be set for Calc II.

El título del comentario se explica solo. Ya había tenido contacto con la colección (con "The Humongous Book of Geometry Problems") y tengo una muy buena opinión de ellos (amplios, detallados, lenguaje accesible y ¡montones de problemas!), así que en cuanto me dijeron que impartiría una clase de Cálculo en preparatoria, no lo pensé dos veces para adquirirlo. No decepciona, será un excelente recurso para apoyar mis notas de clase

I highly recommend this book to anyone taking a first year university calculus course. It covered virtually every concept in my first year calculus course. Also, it not only contains solutions for various calculus problems but demonstrated the methods used to solve them.