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About this book :-
Analytic Geometry with Calculus written by
Robert C. Yates
In recent years analytic geometry and the calculus have been combined into one course for the first or second year of college mathematics, and several excellent texts have been published for this purpose. However, these texts give primary emphasis to the calculus with a correspondingly reduced content in analytic geometry. As a consequence, many students are not acquiring a sound knowledge of analytic facts and techniques. For this reason, this book emphasizes a full-bodied treatment of analytic geometry in which the fundamental principles of calculus are introduced and used in a supporting role. The result is a text, to follow algebra and trigonometry, in which the student is more adequately prepared for the subject matter of calculus.
Certain features of the book are listed here as a guide to the reader before he begins a detailed study of the text. In the geometry of the plane, rectangular and polar coordinates are introduced at the same time and used interchangeably throughout. Lines are characterized by direction numbers for wider application and to facilitate transition to three-space geometry.
The concepts of derivative and its inverse are presented early so that their applications to direction of a curve, motion of points, plane areas, tangents and normals to surfaces and curves in three-space, and volumes bounded by surfaces considerably enhance the subject matter. Discussion of the conies begins with the fundamental consideration of plane sections of a right circular cone, thus establishing their proper designation as conic sections.
The customary `higher plane' curves make their natural appearance as important loci connected with various mechanical devices such as cams, gears, and linkages. There are treatments of diameters of the conics and diametral planes of the quadrics which provide a firm foundation for further study of geometry. The usual treatment of transformations is amplified and extended to plane mappings, some given in matrix form. Ruled surfaces are studied and attention is focused upon their important application in the construction of space gears.
This book contains ample material for a full semester course of four hours a week or for a trimester of five, lours a week. For a shorter course of three semester hours, certain sections (indeed, whole chapters) marked with stars may be omitted without discontinuity. Some of these sections, however, contain material that may well stimulate interest and should not be omitted without considering the student's future.
The book has been written for the student. It is supposed that this is his first introduction to analytic geometry, and to calculus. However, it is assumed that he has some knowledge of algebra (with determinants) and of trigonometry. The concepts of limit and derivative are presented in a manner to give the student clear comprehension and understanding. The formalized 'epsilon-delta' language is left to a later period when the student will be more mature and capable of better appreciation. However, halftruths and twilight meanings have been avoided.
Book Detail :-
Title: Analytic Geometry with Calculus
Edition:
Author(s): Robert Carl Yates
Publisher: Prentice-Hall
Series: Mathematics series
Year: 1961
Pages: 258
Type: PDF
Language: English
ISBN:
Country: US
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About Author :-
Author Robert C. Yates is American math expert. He was professoer of University of South Florida.
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Book Contents :-
Analytic Geometry with Calculus written by
Robert C. Yates
cover the following topics.
I.THE PLANE
1. The Real Number System-Graphs
2. Measures
3. Variables, Functions, Limits, Continuity
4. The Derivative
5. Functions Whose Derivatives Are Known
6. The Straight Line
7. The Circle
8. Conics
9. The Conies: Their Properties and Applications
10. Some Mechanical Motions and Loci
11. Transformations
12. * Mapping
II.THREE -Space
13. Coordinate Systems-Measures
14. Planes and Lines
15. Surfaces and Curves
16. Tangents and Normals
17. Special Surfaces
18. * Volumes
19. Quadric Surfaces
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