Calculus and Graphs: Simplified for a First Brief Course

From the PREFACE
THE importance of the natural sciences is so generally recognized as to need no emphatic statement. Nor is it necessary to point out the dependence of the sciences upon the study and knowledge of mathematics. This dependence is closer and more direct in the case of calculus than in the case of any other branch of mathematics, unless, perhaps, we except elementary algebra and trigonometry. It is primarily for the purpose of making the elements of the calculus directly and familiarly available to students of physics, chemistry and other sciences that the present book is written. At the same time it is hoped that the book will be found well adapted to the use of those who wish an elementary knowledge of calculus for its cultural value.
No knowledge of Analytic Geometry is assumed on the part of students using the present text. On the other hand the idea of coordinate axes and their use in the graphical representation and study of simple algebraic and transcendental functions is introduced in the first chapter and used continually throughout the work. The student becomes familiar with the fundamental ideas of analytic geometry, learns to use both algebraic and geometric methods in the study of functions, and becomes acquainted with the forms and equations of simple curves without definition of those curves or detailed study of their properties. The student thus acquires all the knowledge of analytic geometry necessary to an understanding of the elements of calculus; and assuming on his part a knowledge of elementary algebra and trigonometry, the calculus is made available for a first college course.
Such a course, the writer believes, is not only more useful but also more interesting and simple than a first course in analytic geometry. It is not intended, however, that the present work should replace the study of analytic geometry, the importance of which should not be underrated, but that the study of the latter subject should simply be deferred until the more immediately important subject, the calculus, has been acquired.
The author has striven to present the subject in as simple a way as possible. The aim has been to make the student understand the subject; not to write a book that would satisfy meticulous mathematical pedantry. In so doing the author may have in places sacrificed logical detail to simplicity of presentation, but never, he hopes; accuracy of statement. In the opinion of the writer a too rigidly logical proof with its paraphernalia of subscripted Greek letters is out of place in an elementary first course in calculus, for the reason that the student never understands such a proof. Or if by arduous effort he does grasp its meaning it is at the expense-in time and labor-of other things that are more important and far more useful.
-L. M. Passano.