{"product_id":"2940016794112","title":"Hyperbolic Functions (illustrated)","description":"This compendium of hyperbolic trigonometry was first published as a chapter in Merriman and Woodward’s Higher Mathematics. There is reason to believe that it supplies a need, being adapted to two or three different types of readers. \u003cbr\u003e\u003cbr\u003eCollege students who have had elementary courses in trigonometry, analytic geometry, and differential and integral calculus, and who wish to know something of the hyperbolic trigonometry on account of its important and historic relations to each of those branches, will, it is hoped, find these relations presented in a simple and comprehensive way in the first half of the work. Readers who have some interest in imaginaries are then introduced to the more general trigonometry of the complex plane, where the circular and hyperbolic functions merge into one class of transcendent, the singly periodic functions, having either a real or a pure imaginary period. For those who also wish to view the subject in some of its practical relations, numerous applications have been selected so as to illustrate the various parts of the theory, and to show its use to the physicist and engineer, appropriate numerical tables being supplied for these purposes.\u003cbr\u003e\u003cbr\u003eWith all these things in mind, much thought has been given to the mode of approaching the subject, and to the presentation of fundamental notions, and it is hoped that some improvements are discernible. For instance, it has been customary to define the hyperbolic functions in relation to a sector of the rectangular hyperbola, and to take the initial radius of the sector coincident with the principal radius of the curve; in the present work, these and similar restrictions are discarded in the interest of analogy and generality, with a gain in symmetry and simplicity, and the functions are defined as certain characteristic ratios belonging to any sector of any hyperbola. Such definitions, in connection with the fruitful notion of correspondence of points on conics, lead to simple and general proofs of the addition-theorems, from which easily follow the conversion-formulas, the derivatives, the Maclaurin expansions, and the exponential expressions. The proofs are so arranged as to apply equally to the circular functions, regarded as the characteristic ratios belonging to any elliptic sector. For those, however, who may wish to start with the exponential expressions as the definitions of the hyperbolic functions, the appropriate order of procedure is indicated on page 27, and a direct mode of bringing such exponential definitions into geometrical relation with the hyperbolic sector is shown in the Appendix\u003cbr\u003e\u003cbr\u003eCONTENTS:\u003cbr\u003e1 Correspondence of Points on Conics\u003cbr\u003e2 Areas of Corresponding Triangles\u003cbr\u003e3 Areas of Corresponding Sectors\u003cbr\u003e4 Charactersitic Ratios of Sectorial Measures\u003cbr\u003e5 Ratios Expressed as Triangle-measures\u003cbr\u003e6 Functional Relations for Ellipse\u003cbr\u003e7 Functional Relations for Hyperbola\u003cbr\u003e8 Relations Among Hyperbolic Functions\u003cbr\u003e9 Variations of the Hyperbolic Functions\u003cbr\u003e10 Anti-hyperbolic Functions\u003cbr\u003e11 Functions of Sums and Difference\u003cbr\u003e12 Conversion Formulas\u003cbr\u003e13 Limiting Ratios\u003cbr\u003e14 Derivatives of Hyperbolic Functions\u003cbr\u003e15 Derivatives of Anti-hyperbolic Functions\u003cbr\u003e16 Expansion of Hyperbolic Functions\u003cbr\u003e17 Exponential Expressions\u003cbr\u003e18 Expansion of Anti-functions\u003cbr\u003e19 Logarithmic Expression of Anti-Functions\u003cbr\u003e20 The Gudermanian Function\u003cbr\u003e21 Circular Functions of Gudermanian\u003cbr\u003e22 Gudermanian Angle\u003cbr\u003e23 Derivatives of Gudermanian and Inverse\u003cbr\u003e24 Series for Gudermanian and its Inverse\u003cbr\u003e25 Graphs of Hyperbolic Functions\u003cbr\u003e26 Elementary Integrals\u003cbr\u003e27 Functions of Complex Numbers\u003cbr\u003e28 Addition-Theorems for Complexes\u003cbr\u003e29 Functions of Pure Imaginaries\u003cbr\u003e30 Functions of x + iy in the Form X + iY\u003cbr\u003e31 The Catenary\u003cbr\u003e32 Catenary of Uniform Strength.\u003cbr\u003e33 The Elastic Catenary\u003cbr\u003e34 The Tractory\u003cbr\u003e35 The Loxodrome\u003cbr\u003e36 Combined Flexure and Tension\u003cbr\u003e37 Alternating Currents\u003cbr\u003e38 Miscellaneous Applications\u003cbr\u003e39 Explanation of Tables\u003cbr\u003e40 Appendix\u003cbr\u003e40.1 Historical and Bibliographical\u003cbr\u003e40.2 Exponential Expressions as Definitions","brand":"McMahon","offers":[{"title":"Default Title","offer_id":47101628612848,"sku":"2940016794112","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940016794112_p0.jpg?v=1763641429","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940016794112","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}