In writing this text, we identified content in the calculus curriculum that consistently
presents challenges to our students. We made organizational changes to the standard presentation
of these topics or slowed the pace of the narrative to facilitate students’ comprehension
of material that is traditionally difficult. Two noteworthy modifications appear in
the material for Calculus II and Calculus III, as outlined below.
Often appearing near the end of the term, the topics of sequences and series are the
most challenging in Calculus II. By splitting this material into two chapters, we have
given these topics a more deliberate pace and made them more accessible without adding
significantly to the length of the narrative.
There is a clear and logical path through multivariate calculus, which is not apparent
in many textbooks. We have carefully separated functions of several variables from
vector-valued functions, so that these ideas are distinct in the minds of students. The book
culminates when these two threads are joined in the last chapter, which is devoted to vector
calculus.
Accuracy Assurance
One of the challenges we face with a first edition is ensuring the book meets the high
standards of accuracy that instructors expect. In developing the predecessor to this book,
more than 200 mathematicians reviewed the manuscript for accuracy, level of difficulty,
and effective pedagogy. Additionally, nearly 1000 students participated in class-testing
this book before publication. A team of mathematicians carefully examined each example,
exercise, and figure in multiple rounds of editing, proofreading, and accuracy checking. In
this expanded version, we have incorporated improvements recommended by professors
using the initial version of this book at colleges and universities across the country
In writing this text, we identified content in the calculus curriculum that consistently
presents challenges to our students. We made organizational changes to the standard presentation
of these topics or slowed the pace of the narrative to facilitate students’ comprehension
of material that is traditionally difficult. Two noteworthy modifications appear in
the material for Calculus II and Calculus III, as outlined below.
Often appearing near the end of the term, the topics of sequences and series are the
most challenging in Calculus II. By splitting this material into two chapters, we have
given these topics a more deliberate pace and made them more accessible without adding
significantly to the length of the narrative.
There is a clear and logical path through multivariate calculus, which is not apparent
in many textbooks. We have carefully separated functions of several variables from
vector-valued functions, so that these ideas are distinct in the minds of students. The book
culminates when these two threads are joined in the last chapter, which is devoted to vector
calculus.
Accuracy Assurance
One of the challenges we face with a first edition is ensuring the book meets the high
standards of accuracy that instructors expect. In developing the predecessor to this book,
more than 200 mathematicians reviewed the manuscript for accuracy, level of difficulty,
and effective pedagogy. Additionally, nearly 1000 students participated in class-testing
this book before publication. A team of mathematicians carefully examined each example,
exercise, and figure in multiple rounds of editing, proofreading, and accuracy checking. In
this expanded version, we have incorporated improvements recommended by professors
using the initial version of this book at colleges and universities across the country
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