Compact, Structured Exposition
Taalman and Kohn provide compact instruction on the important concepts of calculus in a linear, straightforward, and predictable format. Each section begins with uncluttered exposition that introduces and explains the key concepts (definitions, short examples and figures, and key theorems with proofs). The section is followed by more complex examples that prepare students for the exercise sets.
An Awareness of Students’ Learning and Study Habits
The authors understand how students use a textbook and have crafted their book to accommodate students’ learning styles. Students who want to read for understanding before attempting the exercises will appreciate the short, clear explanations. Students who want to tackle exercises first can look back to calculation-based examples and compact exposition for guidance. For these students, Concept and Proof exercises test comprehension of the definitions and theory.
Easy Proofs
Every theorem is discussed as a development that requires justification. The text always makes clear what is proved and what is left to the exercises or to future mathematics courses. Every set of exercises includes a range of accessible proofs, some based on the reading and others focusing on special cases that illustrate basic concepts.
Categorized Exercises
Exercises reflect concepts and skills introduced in the section examples; but also test student understanding of the development of the material and the reading itself and. Each exercise set includes the following categories of problems: Thinking Back, Concepts, Skills, Applications, Proofs, and Thinking Forward. Each chapter concludes with a set of Chapter Review exercises.