Review Great Calculus book
Student Solutions Manual for Stewart's Single Variable Calculus Kindle Edtion by Stewart
Student Solutions Manual for Calculus by Steve Rigdon Overview
This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being excessively rigorous, up-to-date without being faddish. Maintains a strong geometric and conceptual focus. Emphasizes explanation rather than detailed proofs. Presents definitions consistently throughout to maintain a clear conceptual framework. Provides hundreds of new problems, including problems on approximations, functions defined by tables, and conceptual questions. Ideal for readers preparing for the AP Calculus exam or who want to brush up on their calculus with a no-nonsense, concisely written book. --This text refers to an out of print or unavailable edition of this title.
Student Solutions Manual for Calculus by Steve Rigdon Review
When I was 15, this was the book that I taught myself Calculus from. Now that I'm a professor, this is the book that I use to teach Calculus. In this review I will give the pros and cons of using this book from both a student's and teacher's perspective.
A Student's Perspective
When learning Calculus, I read every page of this book and did every problem. Students will complain that examples and discussion in each chapter seem inadequate to do all of the problems at the end of the section. I feel that this is part of the design of this book. The problems are intended to be instructional. Indeed this book has a corresponding student solutions manual that helps students to check their work and see if they are "getting it". The problems in the book range from extremely elementary up to moderately challenging. If, instead of instructional problems, this book had given enough examples and text to explain all of the ideas, it would have to be over 2000 pages long. Students should think of the problems in each section as being part of the instruction instead of problems to test previously acquired skills.
When teaching myself from this book, I was able to do all but a few of the problems. Granted I had to spend a considerable amount of time struggling with some of them, but for a talented and dedicated student, every problem in the book is accessible and most are extremely instructive. I should also mention that the book is very well written. Having never actually read a math text book from cover to cover back then, I didn't have too much problem tackling this one. It's very rare that a math text be thorough, informative, and easy to read. This one manages to be all three.
The main drawback of the book is that the students solutions manual is absolutely essential and will be an additional cost. Even if money is tight, as it often is for students, make certain that you buy this manual.
A Teacher's Perspective
As I said above, the problems in this book are intended to be instructional. For this reason it is imperative that a teacher not just lecture from the text and examples, but dig into the problems and carefully choose the most instructive ones for in-class presentations or homework assignments. If you only lecture from the text and examples, you'll only be teaching your class a small fraction of what this book has to offer. If you use this for a course, do as many examples as you have time for. I dedicate one lecture per week to doing nothing but working problems. It might be best to work though the even numbered problems for your class, as the odd numbered ones all appear in the student solutions manual.
The layout of the book is a little bit flawed. This book is aimed at three semester Calculus sequences in state universities and liberal arts colleges. It is not a meant to challenge exceptionally bright students. For this reason parts of chapter 2 seem inappropriate- specifically the sections on the rigorous definition of limits and continuity. If you're teaching a calculus course to non-math majors at modest universities, why would you force students to wade through the muck of mathematical proofs of continuity and existence of limits? In my experience the students absolutely hate this part of the course and gain nothing from it. If you have a few bright kids in your class, you can work with them on an independent study of the more theoretical areas such as this. Also, there are few chapters in the book that are out of place. For example, the chapter on integrating to find the volumes and surface areas of solids of revolution comes way too early while the chapters on transcendental functions, inverse functions, and L'Hopital's Rule come way to late.
Overall the presentation of new ideas is very good in this book, with one notable exception. The book introduces the natural logarithm (ln x) through it's definition in terms of the antiderivative of 1/x. From there it uses the inverse function theorem to derive the exponential function and it's properties. I, and my students, find it more natural to define the Euler number, e, in terms of continuously compounded interest, and then derive the natural logarithm and its properties from the exponential function. It's a matter of taste, but the later approach seemed more lucid to my students. You may want to supplement your lectures in this way.
One of my favorite features of this book is that not only does it cover all the material from a traditional three semester Calculus sequence, but it also has chapters on analytical and numerical solutions to ordinary differential equations as well as an appendix containing more theoretical material for brighter students. If you find yourself teaching an unusually talented bunch of kids, the appendix on mathematical induction as well as the aforementioned sections on ODEs and proofs of continuity and existence of limits can make great supplements to challenge those eager to dive into mathematics.
A Student's Perspective
When learning Calculus, I read every page of this book and did every problem. Students will complain that examples and discussion in each chapter seem inadequate to do all of the problems at the end of the section. I feel that this is part of the design of this book. The problems are intended to be instructional. Indeed this book has a corresponding student solutions manual that helps students to check their work and see if they are "getting it". The problems in the book range from extremely elementary up to moderately challenging. If, instead of instructional problems, this book had given enough examples and text to explain all of the ideas, it would have to be over 2000 pages long. Students should think of the problems in each section as being part of the instruction instead of problems to test previously acquired skills.
When teaching myself from this book, I was able to do all but a few of the problems. Granted I had to spend a considerable amount of time struggling with some of them, but for a talented and dedicated student, every problem in the book is accessible and most are extremely instructive. I should also mention that the book is very well written. Having never actually read a math text book from cover to cover back then, I didn't have too much problem tackling this one. It's very rare that a math text be thorough, informative, and easy to read. This one manages to be all three.
The main drawback of the book is that the students solutions manual is absolutely essential and will be an additional cost. Even if money is tight, as it often is for students, make certain that you buy this manual.
A Teacher's Perspective
As I said above, the problems in this book are intended to be instructional. For this reason it is imperative that a teacher not just lecture from the text and examples, but dig into the problems and carefully choose the most instructive ones for in-class presentations or homework assignments. If you only lecture from the text and examples, you'll only be teaching your class a small fraction of what this book has to offer. If you use this for a course, do as many examples as you have time for. I dedicate one lecture per week to doing nothing but working problems. It might be best to work though the even numbered problems for your class, as the odd numbered ones all appear in the student solutions manual.
The layout of the book is a little bit flawed. This book is aimed at three semester Calculus sequences in state universities and liberal arts colleges. It is not a meant to challenge exceptionally bright students. For this reason parts of chapter 2 seem inappropriate- specifically the sections on the rigorous definition of limits and continuity. If you're teaching a calculus course to non-math majors at modest universities, why would you force students to wade through the muck of mathematical proofs of continuity and existence of limits? In my experience the students absolutely hate this part of the course and gain nothing from it. If you have a few bright kids in your class, you can work with them on an independent study of the more theoretical areas such as this. Also, there are few chapters in the book that are out of place. For example, the chapter on integrating to find the volumes and surface areas of solids of revolution comes way too early while the chapters on transcendental functions, inverse functions, and L'Hopital's Rule come way to late.
Overall the presentation of new ideas is very good in this book, with one notable exception. The book introduces the natural logarithm (ln x) through it's definition in terms of the antiderivative of 1/x. From there it uses the inverse function theorem to derive the exponential function and it's properties. I, and my students, find it more natural to define the Euler number, e, in terms of continuously compounded interest, and then derive the natural logarithm and its properties from the exponential function. It's a matter of taste, but the later approach seemed more lucid to my students. You may want to supplement your lectures in this way.
One of my favorite features of this book is that not only does it cover all the material from a traditional three semester Calculus sequence, but it also has chapters on analytical and numerical solutions to ordinary differential equations as well as an appendix containing more theoretical material for brighter students. If you find yourself teaching an unusually talented bunch of kids, the appendix on mathematical induction as well as the aforementioned sections on ODEs and proofs of continuity and existence of limits can make great supplements to challenge those eager to dive into mathematics.
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