If you like abstraction you can dive headlong into functional analysis and learn about semigroups of operators. It could be action from the platform, personal decision by the review author, part of an entire account closure, even some data error on our part, etc. Differential equations form an essential basis for my profession, and in general that is how I use them: for work. Not only classical theory, but also the main developments of modern times are covered. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation.
The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians. They, not only, seem to realize that there might be 1 or 2 people out that there that didn't get straight A's in all their previous math classes, but there might be a few of us that missed an important topic here or there in our math classes. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians. I could expound praise for this book ad infinitum; it's one of the best values to be offered anywhere. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. Very minimal wear and tear.
Anyways you can purchase it used for pennies. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences. There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. In the process of working on problems like the metrization problem, topologists including Steen and Seebach have defined a wide variety of topological properties. Includes 350 problems and solution.
There are 65 lessons in the 800+ pages of this book. Basic calculus, with knowledge of differentiation and integration techniques are the only prerequisites. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations. This book came up in a recommendation, and I decided to try it after reading all the positive reviews about it. No specific knowledge beyond the usual introductory courses is necessary. Book Description Dover Publications Inc. I would say it is a good book for those in engineering, sciences, or mathematics.
This particular edition is in a Paperback format. Instead, we ask that you. The rest of the book is devoted chiefly to the stability of nonlinear systems, including issues of stability related to perturbations; periodic solutions of two-dimensional systems and the Poincaré-Bendixson theorem; and the stability of the equilibrium point. I'm not quite grasping the relation here between the two subjects. Additional subjects include integral manifolds of equations with a small parameter, periodic systems with a small parameter, alternative problems for the solution of functional equations, and the direct method of Liapunov. Compendious and catholic, the book contains 65 lessons organized into 12 chapters. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works.
This is one of those very rare books that was written with the self taught student in mind, be it either accidental or intentional. When I studied differential equations in class at the university, the text was not too well written and the course content followed the text. Label: Dover Publications, Dover Publications, Produktgruppe: Book, Publiziert: 1985-10-01, Freigegeben: 1985-10-01, Studio: Dover Publications, Verkaufsrang: 17147 Platform order number Amazon. But will substituting Strogatz's book for the traditional approach put me at a disadvantage later when studying higher-level math? Topics include the existence and uniqueness theorem, behavior of characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. May be very minimal identifying marks on the inside cover. For forty years, I have been opening my copy of this book randomly to any section and working whatever problem happened to be there. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application.
Suitable for graduate students as well as scientists, technologists, and mathematicians. Mathematics is supposed to be fun. It was convoluted, spending whole pages trying to explain a concept, chock full of referrals to formulas a few pages back, interspersed with pretty pictures. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. Please be polite and civil when commenting, and always follow. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.
Category: Mathematics Author : Earl A. Its highlight is a scholarly treatment of the stability of dynamical systems, including the absolute stability problem. The problem sets were put together very well--there are lots of problems and they start out easy and get harder. Unabridged and corrected Dover 1985 republication of the work originally published by Harper and Row Publishers, 1963. As the authors indicate in the introduction, you should read the book with a pencil in hand, following along with the examples. Where my text book obviously goes to great lengths to condense 3 or 4 concepts into one, brief, explanation and example; the authors of this book honestly take as much space as they need to. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.
Subsequent chapters review results regarding the existence and uniqueness of solutions of ordinary differential equations; matrix analysis of the linear system of differential equations; and boundary value problems. Although I it doesn't water stuff down either. It's also aimed toward scientists and engineers with practical applied examples. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals.
If one is even remotely interested in learning about differential equations, with or without a solid mathematical background although calculus, obviously, is needed , Ordinary Differential Equations is a great assest to anyone's mathematical library, and Dover publications, as usual, makes this text very affordable. The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. It allows one to understand the overall behavior of a system in phase space without finding a closed-form solution or solving it numerically. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations. Sapterstone's text this semester; it's not bad, fairly concise. Explores integrating factors; dilution and accretion problems; Laplace Transforms; Newton's Interpolation Formulas, more. Each chapter is complemented with a series of well-chosen problems.