Preface
A free and open-source calculus
Several fundamental ideas in calculus are more than 2000 years old. As a formal
subdiscipline of mathematics, calculus was first introduced and developed in the late 1600s,
with key independent contributions from Sir Isaac Newton and Gottfried Wilhelm Leibniz.
Mathematicians agree that the subject has been understood rigorously since the work of
Augustin Louis Cauchy and Karl Weierstrass in the mid 1800s when the field of modern
analysis was developed, in part to make sense of the infinitely small quantities on which
calculus rests. Hence, as a body of knowledge calculus has been completely understood
by experts for at least 150 years. The discipline is one of our great human intellectual
achievements: among many spectacular ideas, calculus models how objects fall under
the forces of gravity and wind resistance, explains how to compute areas and volumes of
interesting shapes, enables us to work rigorously with infinitely small and infinitely large
quantities, and connects the varying rates at which quantities change to the total change
in the quantities themselves.
While each author of a calculus textbook certainly offers her own creative perspective
on the subject, it is hardly the case that many of the ideas she presents are new. Indeed, the
mathematics community broadly agrees on what the main ideas of calculus are, as well as
their justification and their importance; the core parts of nearly all calculus textbooks are
very similar. As such, it is our opinion that in the 21st century – an age where the internet
permits seamless and immediate transmission of information – no one should be required
to purchase a calculus text to read, to use for a class, or to find a coherent collection of
problems to solve. Calculus belongs to humankind, not any individual author or publishing
company. Thus, a main purpose of this work is to present a new calculus text that is free.
In addition, instructors who are looking for a calculus text should have the opportunity to
download the source files and make modifications that they see fit; thus this text is opensource. Since August 2013, Active Calculus has been endorsed by the American Institute of
Mathematics and its Open Textbook Initiative: http://aimath.org/textbooks/.
Because the text is free, any professor or student may use the electronic version of the
text for no charge. A .pdf copy of the text may be obtained by download from
http://gvsu.edu/s/xr,
vii
A free and open-source calculus
Several fundamental ideas in calculus are more than 2000 years old. As a formal
subdiscipline of mathematics, calculus was first introduced and developed in the late 1600s,
with key independent contributions from Sir Isaac Newton and Gottfried Wilhelm Leibniz.
Mathematicians agree that the subject has been understood rigorously since the work of
Augustin Louis Cauchy and Karl Weierstrass in the mid 1800s when the field of modern
analysis was developed, in part to make sense of the infinitely small quantities on which
calculus rests. Hence, as a body of knowledge calculus has been completely understood
by experts for at least 150 years. The discipline is one of our great human intellectual
achievements: among many spectacular ideas, calculus models how objects fall under
the forces of gravity and wind resistance, explains how to compute areas and volumes of
interesting shapes, enables us to work rigorously with infinitely small and infinitely large
quantities, and connects the varying rates at which quantities change to the total change
in the quantities themselves.
While each author of a calculus textbook certainly offers her own creative perspective
on the subject, it is hardly the case that many of the ideas she presents are new. Indeed, the
mathematics community broadly agrees on what the main ideas of calculus are, as well as
their justification and their importance; the core parts of nearly all calculus textbooks are
very similar. As such, it is our opinion that in the 21st century – an age where the internet
permits seamless and immediate transmission of information – no one should be required
to purchase a calculus text to read, to use for a class, or to find a coherent collection of
problems to solve. Calculus belongs to humankind, not any individual author or publishing
company. Thus, a main purpose of this work is to present a new calculus text that is free.
In addition, instructors who are looking for a calculus text should have the opportunity to
download the source files and make modifications that they see fit; thus this text is opensource. Since August 2013, Active Calculus has been endorsed by the American Institute of
Mathematics and its Open Textbook Initiative: http://aimath.org/textbooks/.
Because the text is free, any professor or student may use the electronic version of the
text for no charge. A .pdf copy of the text may be obtained by download from
http://gvsu.edu/s/xr,
vii