Foundations of Infinitesimal Calculus
by K.D. Stroyan
Publisher: Academic Press, Inc. 1997
Number of pages: 182
This book of mathematical 'background' shows how to fill in the mathematical details of the main topics from the course. These proofs are completely rigorous in the sense of modern mathematics - technically bulletproof. We wrote this book of foundations in part to provide a convenient reference for a student who might like to see the 'theorem - proof' approach to calculus.
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by Viktor Blasjo - Intellectual Mathematics
A concise textbook covering precalculus through vector calculus and differential equations using informal infinitesimal reasoning. Always gives the most illuminating proofs possible, while standard books obscure key ideas under pedantic formalism.
by Gregory Hartman, et al. - APEXcalculus.com
A calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now. The explanations of new concepts is clear, written for someone who does not yet know calculus.
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 Dan Sloughter
The book is on sequences, limits, difference equations, functions and their properties, affine approximations, integration, polynomial approximations and Taylor series, transcendental functions, complex plane and differential equations.