xi
Preface
is text covers multi-variable integral and differential calculus, presuming familiarity with the
single variable techniques from the precursor texts Fast Start Differential Calculus and Fast Start
Differential Calculus. e texts were developed for a course that arose from a perennial complaint
by the physics department at the University of Guelph that the introductory calculus courses
covered topics roughly a year after they were needed. In an attempt to address this concern,
a multi-disciplinary team created a two-semester integrated calculus and physics course. is
book covers the integral calculus topics from that course as well a material on the behavior of
polynomial function. e philosophy of the course was that the calculus will be delivered before
it is needed, often just in time, and that the physics will serve as a substantial collection of
motivating examples that will anchor the student’s understanding of the mathematics.
e course has run three times before this text was started, and it was used in draft form
for the fourth offering of the course, and then for two additional years. ere is a good deal of
classroom experience and testing behind this text. ere is also enough information to confirm
our hypothesis that the course would help students. e combined drop and flunk rate for this
course is consistently under 3%, where 20% is more typical for first-year university calculus. Co-
instruction of calculus and physics works. It is important to note that we did not achieve these
results by watering down the math. e topics covered, in two semesters, are about half again
as many as are covered by a standard first-year calculus course. at’s the big surprise: covering
more topics faster increased the average grade and reduced the failure rate. Using physics as a
knowledge anchor worked even better than we had hoped.
is text, and its two companion volumes, Fast Start Differential Calculus and Fast Start
Integral Calculus, make a number of innovations that have caused mathematical colleagues to
raise objections. In mathematics it is traditional, even dogmatic, that math be taught in an order
in which no thing is presented until the concepts on which it rests are already in hand. is is
correct, useful dogma for mathematics students. It also leads to teaching difficult proofs to stu-
dents who are still hungover from beginning-of-semester parties. is text neither emphasizes
nor neglects theory, but it does move theory away from the beginning of the course in acknowl-
edgment of the fact that this material is philosophically difficult and intellectually challenging.
e course also presents a broad integrated picture as soon as possible. e text also emphasizes
cleverness and computational efficiency. Remember that “mathematics is the art of avoiding
calculation.”
It is important to state what was sacrificed to make this course and this text work the
way they do. is is not a good text for math majors, unless they get the theoretical parts of
calculus later in a real analysis course. e text is relatively informal, almost entirely example
xii PREFACE
driven, and application motivated. e author is a math professor with a CalTech Ph.D. and
three decades of experience teaching math at all levels from 7th grade (as a volunteer) to graduate
education including having supervised a dozen successful doctoral students. e author’s calculus
credits include calculus for math and engineering, calculus for biology, calculus for business, and
multivariate and vector calculus.
Daniel Ashlock
August 2019
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