Our purpose in writing a calculus text has been to help students learn at first hand that mathematics is the language in which scientific ideas can be precisely formulated, that science is a source of mathematical ideas that profoundly shape the development of mathematics, and that mathematics can furnish brilliant answers to important scientific problems.
The answer is that science and mathematics are growing by leaps and bounds on the research frontier, so what we teach in high school, college, and graduate school must not be allowed to fall too far behind. As mathematician and educators, our goal must be to simplify the teaching of old topics to take room for new ones.
our aim is to foster understanding, not "rigor."
We have worked hard in this revision to show that uniform convergence and continuity are more natural and useful than pointwise convergence and continuity.引自 Preface
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