This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
Mahi: The Story of India's Most Successful Captain charts the dynamic rise of one of India's most talented and charismatic cricketers and captains. From playing tennis-ball cricket in Ranchi and Kharagpur to his patented helicopter shot, Dhoni has come a long way with his grit and determination. With best ODI and Test records among all Indian captains to date, it is his simple and down-to-earth attitude that works wonders for the captain as well as the team.
This book takes a reader on a tour of astronomical phenomena: from the vastness of the interstellar medium, to the formation and evolution of stars and planetary systems, through to white dwarfs, neutron stars, and black holes, the final objects of the stellar graveyard. At its heart, this book is a journey through the evolutionary history of the birth, life, and death of stars, but detours are also made to other related interesting topics. This highly accessible story of the observed contents of our Galaxy includes intuitive explanations, informative diagrams, and basic equations, as needed. It is an ideal guide for undergraduates with some physics and mathematics background who are studying astronomy and astrophysics. It is also accessible to interested laypeople, thanks to its limited equations. Key features: Includes coverage of some of the latest exciting research from the field, including star formation, exoplanets, and black holes Can be utilised as a stand-alone textbook for a one-term course or as a supplementary textbook for a more comprehensive course on astronomy and astrophysics Authored by a team respected for research, education, and outreach Shantanu Basu is an astrophysicist and a professor at The University of Western Ontario, Canada. He is known for research contributions on the formation of gravitationally-collapsed objects in the universe: stars, planets, brown dwarfs, and supermassive black holes. He is one of the originators of the migrating embryo scenario of episodic accretion onto young stars. He has been recognized for his teaching excellence and his contributions to the astronomical community include organizing many conferences and training schools. Pranav Sharma is an astronomer and science historian known for his work on the history of the Indian Space Program. He has curated the Space Museum at the B. M. Birla Science Centre (Hyderabad, India). He is in-charge of the history of Indo-French scientific partnership project supported by the Embassy of France in India. He is a national-award-winning science communicator and has extensively worked on the popularization of astronomy education in India.
The story revolves around three friends - Deep, Pratik and Tarun. Two of them are missing since a decade. Deep has returned back to Kolkata to find them out and to get them back in his life. In his endeavor, he lives his past and unveil the secrets of his life which becomes a life threat to him. The whole story has been narrated by Deep after five years of this venture. The story traverses through two parallel time scales surfing through love, pain of separation and the strings of friendship. The story discloses the presence of a secret society in Kolkata and their involvement in different political situations,the rest remains a secret. His friends have left a hidden pathway to them, but to camouflage from whom? The story goes on traversing the life of the protagonist and his friends, his love and lots of secret. The sacred darkness remains sanctified until the last page is turned.
XaaS: Everything-as-a-Service: The Lean and Agile Approach to Business Growth takes the reader into the bold new world of pay-per-use for a product or service. From the perspective of the customer, the servitization model yields multiple benefits: the consumer can try out the product/service at a relatively low cost, the risk is mitigated, capital expenses can be converted into operating expenses, it is not needed to forecast how often the product/service is used, and only parts of the product/service needed can be used. Similarly, a provider can benefit by having a larger market coverage, steadier stream of revenues, upgrades as and when needed, sharing of fixed assets across consumers, practicing of value-based pricing, and unbundling or bundling utility for consumers using appropriate pricing techniques. However, this 'nanoization' of products/services is tricky, and has to be designed carefully. This book provides a set of recipes to providers to adopt the XaaS model by changing the provider's mindset: dividing the product/service forces the provider to take a value-driven approach to his product/service, and consequently, eliminate all non-value added activities. The requirements of the XaaS model serve both as an objective to the innovation and internal processes of the provider, and as guide to understanding the customer's needs. The book also covers data acquisition, data analysis and synthesis, and data application needs of the XaaS model, with simple examples and case studies from the business world of firms that achieve these objectives successfully.
If you visit Antwerp, the diamond market of the world, you will see for yourself how Indians have taken over the sleepy Belgian town, where bells in the biggest Hindu temple attract thousands of visitors every evening. Global diamond trade is now on a new chapter, and India is playing an important role in that. Diamonds are the second-largest export commodity from India after mineral fuels. With more than 80 per cent of the world's diamonds being cut and polished in Surat, India has become the processing house for the world's diamonds. But how did we get here?In The Diamond Trail, veteran journalist Shantanu Guha Ray charts the course of India's rise to domination in the diamond industry.
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