Schaum's Outline of Calculus, 5th ed. (Schaum's Outline Series)

This outline will work best for those looking for a concise supplement to their course text. The strength of this outline is in the solved problems. The weakness is in the explanation of concepts. As advertised, the book contains over 1100 fully worked problems. These problems are indeed fully worked and looking over them can be of tremendous value if you are struggling with solving particular problems in your class. If you are having a tough time with the concepts rather than the problems of calculus I would not recommend this book. The explanations are kept to a bare minimum and tough topics like delta-epsilon proofs and Reimann Integrals are not explained in detail. For instance, this book will not try to justify why you can set delta equal to epsilon to complete your limit proof, it just tells you to do it (which is exactly what you need to do to solve the problem). In other words, this book will help you solve the problems you need to solve in order to pass your exams, but it will not necessarily help you understand why those solutions work. So please do not buy this thinking it will have fuller conceptual explanations. Its strength is in its fully solved problems.

I first got acquainted with this particular Schaum's outline when I was a senior in high school back in 1975. It was an essential companion through my senior year and through all three semesters of calculus in college. Through its various revisions it has been one of the more valuable Schaum's outlines I have ever encountered, and I would highly recommend it to any calculus student whether you are doing fine with the material or not. If you are struggling, it acts as a study guide with clear explanations, examples, and figures. If you are OK with the material, it supplies plenty of interesting practice problems to prepare you for exams. If your precalculus is weak, the first eight chapters of the book act as an excellent mini review of that material. Chapters nine through 57 take you through the material you will find in a complete sequence of courses on calculus. Chapters 58 and 59 are additional material. Chapter 58 is a sort of applications chapter on masses of variable density, and chapter 59 is a very brief introduction to ordinary differential equations, which would be your next step past calculus in your journey in applied undergraduate mathematics. The only negative I can really speak of is that Chapter 53, on vector differentiation and integration, seems out of place in the book. There is just enough information presented to confuse the average reader. If you are interested in vector calculus, there is an entire excellent Schaum's outline dedicated to that one subject, and I suggest you not read Chapter 53 of this book and purchase the Schaum's outline of Vector Analysis, which goes into suitable detail on the subject. Another tip- after you pass calculus and even after you graduate keep this book around, particularly if you are an engineer. You will find yourself looking up concepts you have forgotten for years to come.

I've worked with several versions of the Schaum's Calculusover the years. This work has excellent coverage of derivatives,integrals, curvilinear motion, polar coordinates, indeterminateforms, indefinite integrals, centroids, arc length, tests fordivergence/convergence, partial derivatives, volumes, tripleintegrals and a host of exotic areas. There are many multi-dimensional diagrams to aid in your understanding of thisfairly complex subject. I did well in Intermediate Calculusgarnering an "A". In addition, the Fundamentals of EngineeringLicensure Exam covered quite a bit of basic and intermediatecalculus. This is an excellent supplementary work to complementthe course textbook and class notes.

I found this book to be a very good supplement to anyone taking a calculus course. The main highlights (and some, but few) lowlights are as follows:The Good:1. LOTS and LOTS of topics covered ranging from limit concepts to l'Hopital's rule to integral tests to multiple integrals, this book covers A LOT (and even a brief intro to differential equations.)2. Enough practice problems to ensure that the reader will comprehend the material (as is the case with most Schaum Outline books).3. Lots of graphs for visual learners.4. A fraction of the price of most calculus books.The Bad:1. The only bad thing I could possibly think of in this book is that it explains vector concepts and differentiation and integration of vector functions and gradient, divergence, and curl, but leaves out Green's and Stokes' theorems (must be covered in the vector analysis Schaum book). For more detail, check out the list of chapter topics on the back cover of the book (it's a pretty thick paragraph)

My instructor had a nervous breakdown about 1 month into an integral calculus class. He spent the rest of the semester discussing his personal problems during class, instead of teaching. He stopped giving tests and cancelled his office hours. We had a midterm, which I failed (with a 28/100), along with the rest of the class. My entire grade hinged on the final exam. I bought this book and spent the last half of the year using this book to teach me integral calculus. Two weeks before the final, the instructuor told the class that he was throwing out the midterm, and that our grade for the class would be based solely on our performance on the final exam.I got a 96/100 on the final, and an "A" for the course. This book saved me. (This sounds ridiculous, I know...but it is absolutely true.)