Difference Equations to Differential Equations - An introduction to calculus
by Dan Sloughter
Number of pages: 599
The study of calculus begins with questions about change. What happens to the velocity of a swinging pendulum as its position changes? What happens to the position of a planet as time changes? What happens to a population of owls as its rate of reproduction changes? Mathematically, one is interested in learning to what extent changes in one quantity affect the value of another related quantity. Through the study of the way in which quantities change we are able to understand more deeply the relationships between the quantities themselves.
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by Thomas I. Vogel
The intuition is useful in dealing with simple examples, but can be a hindrance to deeper understanding of the basic concepts of mathematical analysis. The point of this text is to challenge and refine the intuition of better calculus students.
by H. Jerome Keisler - Bodgen & Quigley
This is a calculus textbook at the college Freshman level based on infinitesimals. This approach puts the ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners than the more common approach via limits.
by Kenneth Kuttler
Calculus and many of its applications are discussed in this book. The reader should have a good understanding of algebra as well as geometry and trigonometry. There is also lots of non standard material, like some theorems of advanced calculus.
by David Guichard - Lyryx
The book covers the standard Calculus I and II courses, with Calculus III under development. It is accessible to first year college and university students. The emphasis in this course is on problems -- doing calculations and story problems.