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Advanced Trigonometric Relations Through Nbic Functions
Bairagi, Nisith K.
, Retired Professor of Structral Engineering, IIT, Bombay.
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PRINTED BOOK DETAILS:
ISBN :
978-81-224-3023-3
Publication Year :
2012
Edition :
1st
Pages :
276
Price :
$ 24.75
Binding : Hardbound
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About the Book: |
In the present book, a new form of trigonometric relations have been presented and discussed on adopting functions named as Nbic functions, created as the combination of circular and hyperbolic functions of several varieties by separating the real and imaginary parts of the product of complex circular and complex hyperbolic functions of simple or higher orders. Though the variations of the Nbic functions are Iimitless, the scope of the present book covers only Single, Double and Triple Nbic functions. Single Nbic functions, being the simplest of all the varieties, already are in extensive use in the solution of differential equations of fourth and eighth order, as the combinations of, sin-cosh, cos-sinh etc., which are often encountered in structural mechanics and elasticity problems.
The characteristics of the Nbic functions, and other various relations in the form of expressions and identities, written in the similar pattern of trigonometry, are presented and discussed systematically with critical remarks. That there exists a very close similarity in the structural pattern of the trigonometric relations of the Nbic functions with the corresponding ones of the year old circular functions and hyperbolic (or exponential) functions, has been established, and wherever possible, the interrelation among the Nbic and other ones are clearly brought into notice.
Circles when described through Nbic functions do not conform to our known Euclidean (full or complete) circles, and so also is the case with hyperbolic functions. Extending this knowledge, a completely new concept of categorizing of circles, has been proposed, and discussed in a full length chapter, in which the hyperbolic, Euclidean and Nbic circles, respectively, are grouped in the incomplete, complete and over complete category of circles.
A large number of typical numerical examples along with full length calculation is provided at the end of each chapter. This is intended to familiarize the details of the theoretical developments, and simultaneously to verify the correctness of the maiden theoretical formulations presented.
Related to the theoretical development of the text material, Appendices are suitably designed and provided at the end of the book. The solution of the problem of geometrical construction of trisection of a plane angle which remained unsolved by any mathematician of the world up till now, since the era of Archimedes, is fruitfully attempted, and is described and discussed on proposing Bairagi's model, in Appendix C.
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About the Author: |
Dr. Nisith K. Bairagi is a structural engineer by profession. He obtained Bachelor degree from Jadavpur University, Kolkata (1963). From BE College, Shibpur, he obtained Master (Civil) degree (1967), and completed Technical Teachers' Traineeship (1968) in the same college. After joining IIT Bombay as a faculty (1971) in Civil Engineering Department, he obtained PhD (Structures) in 1982. Dr. Bairagi was actively engaged in teaching (UG and PG) and research in the field of Structural Mechanics, Plate and Shell Structures, Concrete Structures and Concrete Technology. He retired from IIT Bombay as Professor of Civil Engineering (2004) after an active service period of about 33 plus years.
Dr. Bairagi has several pioneering original contributions to his credit, mention worthy are: on Selfing and Crossing Concept (Concrete Technology), Pre- and Post-twisted R C Beams (Concrete Structures), Shell-Deck Bridges (Bridge Structures). Reference of these works are available in a large number of research papers published in reputed journals in India and abroad, M Tech as well as PhD theses (three PhDs were supervised by Dr. Bairagi on his own concept of Selfing and Crossing), submitted at IIT Bombay. He authored four books in Structural Engineering subjects.
During teaching and research carrier (1971-2004), while handling theory and analysis of structural engineering subjects, the interest generated in circular-hyperbolic type of functions, (which is often used as an important tool for the solution of fourth as well as eighth order differential equations, frequently encountered in structural engineering problems, such as in Beams on Winkler's Foundation and in thin Cylindrical shells), led Dr. Bairagi to search and formulate for a more general type of function of this category. The present book is the result of his search and research.
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Contents: |
Nbic Functions and Nbic Trigonometric RelationsComplex Nbic Function and Associated TopicsDouble Nbic Function, N2(x, y)Triple Nbic Function, N3(x, y)Reciprocal of Complex Nbic FunctionsCircular Representation of Nbic Functions (Nbic Circles)Application of Single Nbic Functions to Structural ProblemsMatrix Representation of Nbic FunctionsConcluding Remarks
Appendices:
Pythagorean Triplets with a Pair of Consecutive NumbersRoots of Polynomial Equations—Application to the Resultants of Force SystemsBairagi's Theorem on Trisection of an AngleNbic Function Tables
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Audience: |
Mathematics,New Releases
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