Calculus (Taalman Kohn)

Book Preface

Calculus books have become full of clutter, distracting margin notes, and unneeded features. This calculus book clears out that clutter so that students can focus on the important ideas of calculus. Our goal was to create a clean, streamlined calculus book that is accessible and readable for students while still upholding the standards required in science, mathematics, and engineering programs, and that is fl exible enough to accommodate different teaching and learning styles.

Linear Flow with Clean Margins

One thing that is distinctive about this calculus book is that it follows a linear writing style. Figures and equations fl ow with the text as part of a clear, structured exposition instead of being scattered about in the margins. We feel that this approach greatly increases the clarity of the book and encourages focused reading.

Exposition Before Calculation

Another distinctive feature of this book is that in each section we have separated the exposition and illustrative examples from the longer, more complicated calculational examples. Including these longer examples separately from the exposition increases fl exibility: Students who want to read and understand the development of the material can do so without being bogged down or distracted by large examples, while students who want to use the book as a reference for looking up examples that are similar to homework problems can also do that.

Examples to Learn From

Within the exposition of each section are short examples that quickly illustrate the concepts being developed. Following the exposition is a set of detailed, in-depth examples that explore both calculations and concepts. We took great pains to provide many steps and illustrations in each example in order to aid the student, including details about how to get started on a problem and choose an appropriate solution method. One of the elements of the book that we are most proud of is the “Checking the Answer” feature, which we have included after selected examples to encourage students to learn how to check their own answers.

Building Mathematics

We were very careful in this book to approach mathematics as a discipline that is developed logically, theorem by theorem. Whenever possible, theorems are followed by proofs that are written to be understood by students. We have included these proofs because they are part of the logical development of the material, but we have clearly labeled and indented each proof to indicate that it can be covered or skipped, according to instructor preference. Each exercise set contains an optional subsection of proofs, many of which are accessible even to beginning students. In addition, we have emphasized the interconnections among topics by providing “Thinking Back” and “Thinking Forward” exercises in each section and “Capstone” problems at the end of each chapter.