Essentials of Ordinary Differential Equations

Science & Math

Agarwal, Ravi P.

Mathematics

McGraw-Hill Education - Europe

Zero indicates the absence of a quantity or a magnitude. It is so deeply rooted in our psyche today that nobody will possibly ask "What is zero?" From the beginning of the very creation of life, the feeling of lack of something or the vision of emptiness/void has been embedded by the creator in all living beings. While recognizing different things as well as the absence of one of these things are easy, it is not so easy to fathom the complete nothingness viz. the universal void. Although we have a very good understanding of nothingness or, equivalently, a zero today, our forefathers had devoted countless hours and arrived at the representation and integration of zero and its compatibility not only with all non-zero numbers but also with all conceivable environments only after many painstaking centuries. Zero can be viewed/perceived in two distinct forms: (i) as a number in our mundane affairs and (ii) as the horrific void or Absolute Reality in the spiritual plane/the ultimate state of mind.  Presented are the reasons why zero is a landmark discovery and why it has the potential to conjure up in an intense thinker the dreadful nothingness unlike those of other numbers such as 1, 2, and 3. Described are the representation of zero and its history including its deeper understanding via calculus, its occurrences and various roles in different countries as well as in sciences/engineering along with a stress on the Indian zero that is accepted as the time-invariant unique absolute zero. This is followed by the significant distinction between mathematics and computational mathematics and the concerned differences between the unique absolute zero and non-unique relative numerical zeros and their impact and importance in computations on a digital computer.Introduces the history of the value of zero and why it was a landmark discoveryDiscusses how zero is used in science and engineering and its use in different countriesExplains how zero affects different mathematics and calculus

Zero: A Landmark Discovery, the Dreadful Void, and the Ultimate Mind

Sen, Syamal K.

Academic Press

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Inequalities for Differential Forms

Ding, Shusen

Nolder, Craig

Springer

1. P. Maslak: Fragmentations by Photoinduced Electron Transfer. Fundamentals and Practical Aspects 2. P.K. Freeman, S.A. Hatlevig: The Photochemistry of Polyhalocompounds, Dehalogenation by Photoinduced Electron Transfer, New Methods of Toxic Waste Disposal 3. J.-P. Soumillion: Photoinduced Electron Transfer Employing Organic Anions 4. A. Albini, E. Fasani, M. Mella: PET-Reactions of Aromatic Compounds 5. G. Pandey: Photoinduced Electron Transfer (PET) in Organic Synthesis 6. R.A. Bissell, A.P. de Silva, H.Q.N. Gunaratne, P.L.M. Lynch, G.E.M. Maguire, C.P. McCoy, K.R.A.S. Sandanayake: Fluorescent PET (Photoinduced Electron Transfer) Sensors

Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topics in Current Chemistry)

O’Regan, Donal

Sahu, D. R.

Chemistry

Ordinary differential equations serve as mathematical models for many exciting real world problems. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections.

An Introduction to Ordinary Differential Equations (Universitext)

An Introduction to Ordinary Differential Equations

Springerverlag New York

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis.  This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields.  This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topological Fixed Point Theory and Its Applications, 6)

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

Ordinary and Partial Differential Equations: With Special Functions, Fourier Series, and Boundary Value Problems (Universitext)

Fixed Point Theory and Applications (Cambridge Tracts in Mathematics, Series Number 141)

This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Meehan, Maria

Cambridge University Press

See the best price to sell, buy, or rent books by Agarwal, Ravi P.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Agarwal, Ravi P.

See the best price to sell, buy, or rent books by Agarwal, Ravi P.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Essentials of Ordinary Differential Equations

Zero: A Landmark Discovery, the Dreadful Void, and the Ultimate Mind

Inequalities for Differential Forms

Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topics in Current Chemistry)

An Introduction to Ordinary Differential Equations (Universitext)

An Introduction to Ordinary Differential Equations

Fixed Point Theory for Lipschitzian-type Mappings with Applications (Topological Fixed Point Theory and Its Applications, 6)

Ordinary and Partial Differential Equations: With Special Functions, Fourier Series, and Boundary Value Problems (Universitext)

Fixed Point Theory and Applications (Cambridge Tracts in Mathematics, Series Number 141)

Fixed Point Theory and Applications (Cambridge Tracts in Mathematics, Series Number 141)