Series Editor: Steven G. Krantz, Washington University in St. Louis
Fast Start Dierential Calculus
Daniel Ashlock, University of Guelph
e three books in the fast start calculus series were developed over a period of ve years with classroom
testing each year at the University of Guelph. e development team included two physics professors
and two senior teaching assistants in math in addition to the author. e books cover dierential and
integral calculus with a selection of topics from advanced calculus including partial derivatives, multiple
integrals, and sequences and series up to Taylor series. e topics track the use of calculus in rst year
physics and can be paired with a physics course that provides an anchor for the mathematical concepts.
Over the rst ve years of use, including three revisions to improve clarity and accuracy, no more than
3% of a class dropped or unked the joint math and physics course. is contrasts with a 12%-20% rate
in the standard calculus course. e topics in the course are ordered in a novel fashion, moving dicult
theoretical material to the later part of the rst semester, and moving quickly to calculus topics with
applications in the physical sciences.
e rst in the fast start calculus series, this book focuses on the dierential calculus. It begins
with a review of algebra and a review of the library of functions that are needed in some programs
and a helpful reference for students in almost any program of study that includes calculus. e text
covers the denition of the derivative, the physical interpretation of the derivative, applications of the
derivative to curve sketching and thus qualitative models, and the use of derivatives in optimization. It
concludes with the technical denitions concerning limits and continuity. is placement is deliberate
as it permits the students to achieve a more appropriate level of mathematical maturity before tackling
these topics and places the material so that it can be excluded from general education courses for which
this topic might be too challenging.
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About SYNTHESIS
This volume is a printed version of a work that appears in the Synthesis
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ASHLOCK FAST START DIFFERENTIAL CALCULUS MORGAN & CLAYPOOL
Series ISSN: 1938-1743
Fast Start Differential Calculus
Synthesis Lectures on
Mathematics and Statistics
Editor
Steven G. Kranz, Washington University, St. Louis
Fast Start Differential Calculus
Daniel Ashlock
2019
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2017
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