Multivariable Calculus: Early Transcendentals

Conceptual Insights encourage the student to develop a conceptual understanding of calculus by explaining important ideas clearly but informally.

Graphical Insights enhance the students' visual understanding by making the crucial connection between graphical properties and the underlying concept.
Assumptions Matter uses short explanations and well-chosen counterexamples to help students appreciate why hypotheses are needed in theorems.
 
Reminders are margin notes that link back to important concepts discussed earlier in the text.
 
Caution notes warn students of common pitfalls they can encounter in understanding the material.

Historical Perspectives are brief vignettes that place key conceptual discoveries and advancements in their historical settings.  They give students a glimpse into past accomplishments of great mathematicians and an appreciation for their significance.
 
Section Summaries summarize a section’s key points in a concise and useful way to emphasize for students what is most important in the section.
 
Section Exercise Sets offer a comprehensive set of exercises closely coordinated with the text. These exercises vary in levels of difficulty from routine, to moderate, to more challenging.  Also included are questions appropriate for written response or use of technology:
• Preliminary Exercises begin each exercise set and need little or no computation.  They can be used to check understanding of key concepts of a section before problems from the exercise set are assigned. 
• Exercises offers numerous problems from the routine drill problems to moderately challenging problems.   These are carefully graded and include many innovative and interesting geometric and real world applications.
• Further Insights and Challenges are more challenging problems that help to extend a section’s material.   
End of Chapter Review Exercises offer a comprehensive set of exercises closely coordinated with the chapter material to provide additional problems for self study or assignments.