Single Variable Calculus I: Early Transcendentals
David Guichard, Whitman College
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This textbook contains 10 chapters and selected exercise answers. The book covers the review of algebra and functions, limit, derivatives, derivative read more
This textbook contains 10 chapters and selected exercise answers. The book covers the review of algebra and functions, limit, derivatives, derivative tests, graphing using the derivative tests, L'Hopital Rule, optimization problem, integration, techniques of integration, calculation of area between curves and volume, first and second order differential equations, polar coordinates and parametric equations. This book contains all the materials needed for Calculus I and most materials for Calculus II. The book offers great explanations of concepts, formula and theories. In particular, it contains some mnemonic keys to help students memorize important rules in the review chapter (first chapter). I really like the author pointing out the misconceptions that students usually have throughout the book and listing the detailed steps of problem solving. I also like the author using color contrasts to label definitions, theorems, and examples. This book does not have index or glossary at the end.
This book has been modified and some exercises and examples are taken from the other book Elementary Calculus: An Approach Using Infinitesimals. Therefore, I believe the majority of the materials should be accurate and unbiased. I haven't used this text yet myself, so I can't identify whether the solutions to the exercises are accurate. The graphs and tables are clean and accurate. The solutions to examples are laid out nicely with detailed steps. The only mistake that I found is on page 133, example 4.40, the right hand side for the third step should be "1-y2x" instead of "-y2x".
This text doesn't contain many real-life examples. But the knowledge included are up-to-date. The structure of the text is definition-theorem-examples, so it will be relatively easy to add real-life examples and implement.
The text is written clearly. The explanations of theorem are precise and in details. The solutions to examples are step by step. The graphs help students to understand the materials. This book doesn't contain enough real-life related examples, so it could be mathematical and technical to non-math major students.
The author did a great job to keep the consistency in terms of language and structure of the book. The book keeps the same color scheme for definitions, theorem and examples. The structure for each chapter each section are consistent.
The text follows the standard Calculus sequence. Each section are 3-6 pages. The book contains enough subheadings and subsections and can be easily divided into smaller reading sections. The text is not overly self-referential.
The organization of the book is excellence. Each section starts with an opening of a problem, and then the author introduces related definitions or theorem, followed by examples. The text spends two chapters to review algebra and function which is necessary for non-math majored students. It introduces asymptotes of graphs in the chapter of applications of derivatives, which is different from the traditional approach that introduces asymptotes in the chapter of limit. This way, students can have a complete knowledge of graphing a function. This text includes linear approximation at the beginning of the chapter of applications of derivatives and introduces related rates at the very end of that chapter. This is also different from other textbooks. This design separates the introduction of derivative and applications of derivative completely. Related rates is a difficult topic in Calculus I. Introducing related rates at the end of derivatives helps students to practice more before getting into it.
This text has no navigation issues. Whenever it refers to previous examples or definitions, the author uses internal hyperlink taking you to the right place. But it would be nice if there is a way to return back to where the reader was after reviewing the referred materials. Some of the figures are not labeled, but they are referred from the text right above.
I didn't notice any grammar mistakes
The text has not many life-related examples. Majority of the examples are mathematical. So the text is not culturally insensitive or offensive in any way.
I personally like this book. It has a very nice structure and detailed explanations to examples. It also points out the misconceptions that students usually have which helps students to grasp the knowledge accurately.
Table of Contents
- Applications of Derivatives
- Techniques of Integration
- Applications of Integration
- Differential Equations
- Polar Coordinates, Parametric Equations
About the Book
The emphasis in this course is on problems—doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems. The more problems you do the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them. You will learn quickly and effectively if you devote some time to doing problems every day. Typically the most difficult problems are story problems, since they require some effort before you can begin calculating. Here are some pointers for doing story problems:
- Carefully read each problem twice before writing anything.
- Assign letters to quantities that are described only in words; draw a diagram if appropriate.
- Decide which letters are constants and which are variables. A letter stands for a constant if its value remains the same throughout the problem.
- Using mathematical notation, write down what you know and then write down what you want to find.
- Decide what category of problem it is (this might be obvious if the problem comes at the end of a particular chapter, but will not necessarily be so obvious if it comes on an exam covering several chapters).
- Double check each step as you go along; don’t wait until the end to check your work.
- Use common sense; if an answer is out of the range of practical possibilities, then check your work to see where you went wrong
About the Contributors
David Guichard is a Professor of Mathematics at Whitman College in Walla Walla, Washington. He received his Ph.D. from the University of Wisconsin, and his research interests include Graph Theory.