Download or read book A Particular Solutions Formula for Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations written by Claude Michael Cassano and published by CreateSpace. This book was released on 2012-01-01 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: A particular solution for any inhomogeneous linear second, third, and fourth order ordinary differential equation is generally determined. Applying what was determined thus; and following by example a particular solution formula for arbitrary order is obtained. Finding a particular solutions to a linear inhomogeneous ordinary differential equation has always been a process of determining homogeneous solutions, and then adding any particular solution of the inhomogeneous equation. The well-known methods of undetermined coefficients and variation of parameters have long been the standard in determining this particular solution. The former has sometimes been considered 'ad-hoc', and both can be intricate. A relatively simple formuila has been found which allows the particular solution to be written and evaluated immediately.
Download or read book Handbook of Exact Solutions for Ordinary Differential Equations written by Valentin F. Zaitsev and published by CRC Press. This book was released on 2002-10-28 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
Download or read book Ordinary Differential Equations written by W. Cox and published by Butterworth-Heinemann. This book was released on 1996-01-05 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts are worked through in detail and the student is encouraged to develop much of the routine material themselves.
Download or read book Ordinary Differential Equations written by Raza Tahir-Kheli and published by Springer. This book was released on 2019-02-05 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.
Download or read book Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Download or read book Ordinary Differential Equations written by Mikhail Leontʹevich Krasnov and published by . This book was released on 1987 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book CK 12 Calculus written by CK-12 Foundation and published by CK-12 Foundation. This book was released on 2010-08-15 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
Download or read book Differential Equations Problem Solver written by David Arterbum and published by Research & Education Assoc.. This book was released on 2012-06-14 with total page 1570 pages. Available in PDF, EPUB and Kindle. Book excerpt: REA’s Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies. The Differential Equations Problem Solver is the perfect resource for any class, any exam, and any problem.
Download or read book Analysis And Differential Equations written by Odile Pons and published by World Scientific Publishing Company. This book was released on 2015-01-19 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered.It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.
Download or read book Ordinary Differential Equations written by Paul DuChateau and published by Harper Perennial. This book was released on 1992 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations written by Anindya Dey and published by CRC Press. This book was released on 2021-09-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations: A Linear Algebra Approach follows an innovative approach of inculcating linear algebra and elementary functional analysis in the backdrop of even the simple methods of solving ordinary differential equations. The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2012-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Download or read book Introduction to Ordinary Differential Equations written by Zane C. Motteler and published by Prindle Weber & Schmidt. This book was released on 1972 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordinary Differential Equations written by H. Gask and published by . This book was released on 1968 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations written by Lothar Collatz and published by John Wiley & Sons. This book was released on 1986 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution by the Method of G C Evans of the Volterra Integral Equation Corresponding to the Initial Value Problem for a Non homogeneous Linear Differential Equation with Constant Coefficients written by Jackson Henry Bello and published by . This book was released on 1972 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first chapter of this thesis, several methods are used to solve an n-th order linear ordinary differential equation with constant coefficients together with n known initial values. The first method is the standard elementary method where the general solution of the differential system is found as a sum of two solutions u and v where u is the solution of the homogeneous part of the ordinary differential equation and v is any particular solution of the nonhomogeneous differential equation. The method is not strong enough to find a particular solution for every function that might be given as the non-homogeneous term of the ordinary differential equation and so we try a more powerful approach for finding v; hence the Lagrange's method of variation of parameters. Following this, the method of Laplace transforms is employed to solve the differential system. In the second chapter the n-th order linear ordinary differential equation is converted into a Volterra integral equation of second kind and in the next chapter, the idea of the resolvent kernel of an integral equation is introduced with some proofs of the existence and convergence of the resolvent kernel of the integral equation. The method of solving the Volterra integral equation by iteration is briefly discussed. The fourth chapter is devoted to solving the Volterra integral equation with convolution type kernel by the method of E.T. Whittaker, but the method is found to be very involved, and as a result, a method suggested by G.C. Evans (1911) is employed in calculating the resolvent kernels for kernels made up of sums of two exponential functions (the method of iteration was applied to the same problem but it was tedious--it took about 20 pages of writing) and finally the method provides an easier way for calculating the resolvent kernel of the Volterra integral equation corresponding to an n-th order linear ordinary differential equation with constant coefficients.
