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ARTHUR SULLIVAN GALE, PH.D.
CHARLES WILLIAM WATKEYS, A.M.
PROFESSORS OF MATHEMATICS
IN THE UNIVERSITY OF ROCHESTER
HENRY HOLT AND COMPANY
This book presents a coherent year's work in mathematics for college freshmen, consisting of a study of the elementary functions, algebraic and transcendental, and their applications to problems arising in various fields of knowledge. The treatment is confined to functions of one variable, with incidental exceptions, and complex values of the independent and dependent variables are excluded. The subject matter includes the essentials of plane trigonometry and topics from advanced algebra, analytic geometry, and calculus.
The text is the result of experiments beginning in 1907–8. It has been used in the classroom since 1913-14, and each year extensive revisions have been made. Hence the content of the course, the order of topics, and the manner of presentation are based upon the experience of several years.
The unity of the course is gained by an explicit analysis of the functions studied, which enables the student to comprehend the purpose of the course as a whole and the nature of the investigation of properties of functions of a given type. This analysis consists of three parts:
First. Relations between a given function and its graph (see pages 42 and 274). Most of these relations are considered in the first chapter so that at the start the student is made aware of a number of questions which will be investigated in studying a particular type of functions.
Second. Relations between pairs of functions and their graphs (see page 152). These geometric transformations are introduced in connection with simple algebraic functions so that they are familiar tools by the time they are needed for the study of transcendental functions.