“…Includes concise and easy-to-follow descriptions of Newton's work on gravity, motion, light, colour and calculus, as well as assessing his continuing legacy..…”
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“…Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. …”
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“…An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. …”
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“…As described in Chapter 3, COMPILE transforms predicate calculus expressions into clause form as required by HERBY and THEO. …”
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“…Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics.…”
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“…The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. …”
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“…This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. …”
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“…The topics covered include: (1) geometry in the oulvasatras; (2) the origins of zero (which can be traced to ideas of lopa in Paoini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kunnaka, Bhavana and Cakravala (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Paoini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhaua (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. …”
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“…The Spaces R, Rk, and CThe Real Numbers RThe Real Spaces RkThe Complex Numbers CPoint-Set Topology Bounded SetsClassification of Points Open and Closed SetsNested Intervals and the Bolzano-Weierstrass Theorem Compactness and Connectedness Limits and Convergence Definitions and First Properties Convergence Results for SequencesTopological Results for Sequences Properties of Infinite SeriesManipulations of Series in RFunctions: Definitions and Limits DefinitionsFunctions as MappingsSome Elementary Complex FunctionsLimits of FunctionsFunctions: Continuity and Convergence Continuity Uniform Continuity Sequences and Series of FunctionsThe DerivativeThe Derivative for f: D1 → RThe Derivative for f: Dk → RThe Derivative for f: Dk → RpThe Derivative for f: D → CThe Inverse and Implicit Function TheoremsReal IntegrationThe Integral of f: [a, b] → RProperties of the Riemann Integral Further Development of Integration TheoryVector-Valued and Line IntegralsComplex IntegrationIntroduction to Complex Integrals Further Development of Complex Line Integrals Cauchy's Integral Theorem and Its Consequences Cauchy's Integral Formula Further Properties of Complex Differentiable Functions Appendices: Winding Numbers Revisited Taylor Series, Laurent Series, and the Residue Calculus Power SeriesTaylor Series Analytic FunctionsLaurent's Theorem for Complex FunctionsSingularitiesThe Residue Calculus Complex Functions as MappingsThe Extended Complex PlaneLineal Fractional TransformationsConformal MappingsBibliographyIndexExercises appear at the end of each chapter.…”
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“…Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. …”
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“…Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics Review of the first edition: This book presents an introduction to differential geometry and the calculus on manifolds with a view on some of its applications in physics. … The present author has succeeded in writing a book which has its own flavor and its own emphasis, which makes it certainly a valuable addition to the literature on the subject. …”
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“…The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. …”
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“…Jet calculus offers a unique mathematical technique to bridge the area of QCD resummation with Monte Carlo parton showers. …”
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“…The problem of the ME in TE is its complex computational calculus, which makes its use problematic in some situations. …”
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“…Supragingival dental calculus, halitosis, and gingival inflammation were also observed. …”
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“…After discharge, he underwent extracorporeal shock wave lithotrity for the left ureteral calculus. He had no recrudescence of the symptoms. …”
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“…However review of the English language medical literature revealed only a few previous reports of jackstone calculus. CASE PRESENTATION: We report a case in which a large jackstone calculus was incidentally detected during the evaluation of 67 year old male presenting with lower urinary tract symptoms. …”
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“…In the present case study, we removed two sialoliths located beneath the mucosa in the posterior and anterior regions of Wharton's duct, respectively. For the posterior calculus, we performed sialolithotomy via an intra-oral approach; thereafter, the small anterior calculus near the duct orifice was removed by hydraulic power. …”
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“…Computed tomography detected a urethral calculus. The calculus was removed surgically. The stone was composed of calcium oxalate. …”
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“…Co-administration of AEMU with ethylene glycol has significantly (p < 0.001) increased the urine volume and the level of calculus inhibitors like magnesium, citrate and decreased the level of calculus promoters like calcium, oxalate, uric acid and urea also decreased in crystalluria in urine. …”
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