DOCUMENT RESUME BD 135 629 SE 021 999 AUTHOR Allen, Frank B.; And Others TITLE Elementary Functions, Student's Text, Unit 21. INSTITUTION Stanford Univ., Calif. School Mathematics Study Group. SPONS AGENCY National Science Foundation, Washington, D.C. PUB DATE 61 NOTE 398p.; For related documents, see SE 021 987-022 002 and ED 130 870-877; Contains occasional light type EDRS PRICE MF-$0.83 HC-$20.75 Plus Postage. DESCRIPTO2S *Curriculum; Elementary Secondary Education; Instruction; *Instructional Materials; Mathematics Education; *Secondary School Mathematics; *Textbooks IDENTIFIERS *Functions (Mathematics); *School Mathematics Study Group ABSTRACT Unit 21 in the SMSG secondary school mathematics series is a student text covering the following topics in elementary functions: functions, polynomial functions, tangents to graphs of polynomial functions, exponential and logarithmic functions, and circular functions. Appendices discuss set notation, mathematical induction, significance of polynomials, area under a polynomial graph, slopes of area functions, the law of growth, approximation and computation of e raised to the x power, an approximation for ln x, measurement of triangles, trigonometric identities and equations, and calculation of sim x and cos x. (DT) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality * * of the microfiche and hardcopy reproductions ERIC makes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original. * *********************************************************************** STUDENT'S TEXT U S OEPARTME NT OF HEALTH. EDUCATION & WELFARE NATIONAL INSTITUTE OF EOUCATION THIS DOCUMENT HAS BEEN REPRO- DUCEO EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN- ATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE. SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITION OR POLICY ELEMEN ARY FUNCTIONS l'it.)I 'I'Tw; Coy: Ai .,AL (J4,-1TE ti SMSG ,..1fINi =.1,(7 11111101111511WRIZENEM 11$11111111EZIEINA SCHOOL MATHEMATICS STUDY GROUP YALE UNIVERSITY PRESS School Mathematics Study Group Elementary Functions Unit 21 3 Elementary Functions Student's Text Prepared under the supervision of the Panel on Sample Textbooks of the School Mathematics Study Group: Frank B. Allen Lyonsownship High School Edwin C. Douglas Taft School Donald E. Richmond Williams College Cha:les E. Rickart Yale University Henry Swain New Tricr Township High School Robert J. Walker Cornell University New Haven and London, Yak University Press Copyright © 1960, 1961 by Yale University. Printed in the United States of America. All rights reserved. This book may not be reproduced, in whole or in part, in any form, without written permissionfrom the publishers. Financial support for the School Mathematics Study Group has been provided by the National Science Foundation. 0 ............ ,- FOREWORD The increasing contribution of mathematics to the culture of the modern world, as well as its importance as a vital part of scientific and humanistic education, has made it essential that the mathematics in our schools be both well selected and well taught. With this in mind, the various mathematical organizations in the United States cooperated in the formation of the School Mathematics Study Group (SMSG). SMSG includes college and univer- sity mathematicians, teachers of mathematics at all levels, experts in education, and representatives of science and technology. The general objective of SMSG is the improvement of the teaching of mathematics in the schools of this country. The National Science Foundation has provided substantial funds for the support of this endeavor. One of the prerequisites for the improvement of the teaching of. mathematics in our schools is an improved curriculum--one which takes account of the increasing use of mathematics in science and technology and in other areas of knowledge and at the same time one which reflects recent advances in mathematics itself. One of the first projects undertaken by SMSG was to enlist agroup of outstanding mathematicians and mathematics teachers toprepare a series of textbooks which would illustrate such an .improved curriculum. The professional mathematicians in SMSG believe that the mathematics presented in this text is valuable for all well-educated citizens in our society to know and that it is important for the precollege student to learn in preparation for advanced work in the field. At the same time, teachers in SMSG believe that it is presented in such a form that it can be readily grasped by students. In most instances the material will have a familiar note, but the presentatioh and the point of view will be different. Some material will be entirely new to the traditional curriculum. This is as it should be, for mathematics is a living and an ever-growing subject, and not a dead and frozen product of antiquity. This healthy fusion of the old and the new should lead students to a better understanding of the basic concepts and structure of mathematics and provide a firmer foundation for understanding and use of mathematics in a scientific society. It is not intended that this book be regarded as the only definitive way of presenting good mathematics to students at this level. Instead, it should be thought of as a:sample of the kind of improved curriculum that we need and as a source of suggestions for the authors of commercial textbooks. It is sincerely hoped that these texts will lead the way toward inspiring a more meaningful teaching of Mathematics, the Queen and Servant of the Sciences. 6 Below are listed the names of all those who participated In any of the writing sessions at which the following SMSO texts were prepared: First Course in Algebra, Geometry, Intermediate Mathematics, Elementary Functions, and Introduction to Matrix Algebra, H.W. Alexander, Earlham College R.C. Jurgensen, Culver Military Academy, F.B. Allen, Lyons Township High School, La Culver, Indiana Grange, Illinois Joseph Lehner, Michigan State University Alexander Beck, Olney High School, Phila- Marguerite Lehr, Bryn Mawr College delphia, Pennsylvania Kenneth Leisenring, University of Michigan E.F. Beckenbach, University of California Howard Levi, Columbia University at Los Angeles Eunice Lewis, Laboratory High School, E.G. Begle, School Mathematics Study Group, University of Oklahoma Yale University M.A. Linton, William Penn Charter School, Paul Berg, Stanford University Philadelphia, Pennsylvania Emil Berger, Monroe High School, St. Paul, A.E. Livingston, University of Washington Minnesota L.H. Loomis, Harvard University Arthur Bernhart, University of Oklahoma R.V. Lynch, Phillips Exeter Academy, R.H. Bing, University of Wisconsin Exeter, New Hampshire A.L. Blakers, University of Western W.K. McNabb, Hockaday School, Dallas, 'Australia Texas A.A. Blank, New York University K.G. Michaels, North Haven High School, Shirley Boselly, Franklin High School, North Haven, Connecticut Seattle, Washington - E.E. Moise, University of Michigan K.E. Brown, Department of Health, Educa- B44p. Northrop, University of Chicago tion, and Welfare, Washington, D.C. 0.T. Peterson, Kansas State Teachers J.M. Calloway, Carleton College College, Emporia, Kansas Hope Chipman, University High School, Ann B.J. Pettis, University of North Carolina Arbor, Michigan R.S. Pieters, Phillips Academy, Andover, R.R. Christian, University of British Massachusetts Columbia H.O. Pollak, Bell Telephone Laboratories R.J. Clark, St. Paul's School, Concord, Walter Prenowitz, Brooklyn College New Hampshire G.B. Price, University of Kansas P.H. Daus, University of California at Los A.L. Putnam, University of Chicago Angeles Persis O. Redgrave, Norwich Free Academy, R.B. Davis, Syracuse University Norwich, Connecticut Charles DePrima, California Institute of Mina Rees, Hunter College Technology D.E. Richmond, Williams College Mary Dolciani, Hunter College C.E. Rickart, Yale University Edwin C. Douglas, The Taft School, Water- Harry Ruderman, Hunter College High School, town, Connecticut New York City Floyd Doons, East High School, Denver, J.T. Schwartz, New York University Colorado O.E. Stanaitis, St. Olaf College E.A. Dudley, North Haven High School, North Robert Starkey, Cubberley High Schools, Haven, Connecticut Palo Alto, California Lincoln Durst, The Rice Institute Phillip Stucky, Roosevelt High School, Floren:e Elder, West Hempstead High School, Seattle, Washington West Hempstead, New York Henry Swain, New Trier Township High W.E. Ferguson, Newton High School, Newton- School, Winnetka, Illinois vine, Massachusetts Henry Syer, Kent School, Kent, Connecticut N.J. Fine, University of Pennsylvania G.B. Thomas, Massachusetts Institute of Joyce D. Fontaine, North Haven High School, Technology North Haven, Connecticut A.W. Tucker, Princeton University F.L. Friedman, Massachusetts Institute of H.E. Vaughan, University of Illinois Technology John Wagner, University of Texas Esther Gassett, Claremofe High School, R.J. Walker, Cornell University Claremore, Oklahoma A.D. Wallace, Tulane University R.K. Getoor, University of Washington E.L. Walters, William Penn Senior High V.H. Haag, Franklin and