The presentation is not as formal mathematics, e. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.
Book Summary: Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations PDEs , namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow.
For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful.
The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.
Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives.
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 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. Book Summary: This book introduces finite difference methods for both ordinary differential equations ODEs and partial differential equations PDEs and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. Book Summary: This is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject.
The prerequisites are calculus, some knowledge of ordinary differential equations, and knowledge of computer programming using Fortran. Normally this should be half of a two semester course, the other semester covering numerical solution of linear systems, inversion of matrices and roots of polynomials.
Neither semester should be a prerequisite for the other. This would prepare the student for advanced topics on numerical analysis such as partial differential equations. We are philosophically opposed to a one semester surveyor "numerical methods" course which covers all of the above mentioned topics, plus perhaps others, in one semester. We believe the student in such a course does not learn enough about anyone topic to develop an appreciation for it. For reference Chapter I contains statements of results from other branches of mathematics needed for the numerical analysis.
The instructor may have to review some of these results. Chapter 2 contains basic results about interpolation. We spend only about one week of a semester on interpolation and divide the remainder of the semester between quadrature and differential equations. Book Summary: Ordinary differential equations ODEs , differential-algebraic equations DAEs and partial differential equations PDEs are among the forms of mathematics most widely used in science and engineering.
Each of these equation types is a focal point for international collaboration and research. Book Summary: With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations.
Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text.
The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation.
This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations. Book Summary: The book discusses the solutions to nonlinear ordinary differential equations ODEs using analytical and numerical approximation methods.
Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs.
Many of the examples and problems are selected from recent papers of varied university and other engineering examinations. BS Grewal higher engineering mathematics is undoubtedly the foremost read and popular engineering mathematics book among Indian students also as in other countries.
The reason is that this bs grewal pdf book may be a complete package of mathematics for any undergraduate engineering branch. Having oceans of exemplary problems and good quality questions, B S Grewal Higher Engineering Mathematics is extremely easy to master mathematics subject at an undergraduate level. This book is written so nicely that you simply will start loving mathematics from the day one; whether you solve it for academics or any competitive examination; directly or indirectly the book is equally important for all the undergraduate and graduate entrance exams.
And remember! Grewal is an Indian academic author and educationist. LearnCreative team attempt to Helping the scholars et al. Thank you. Useless shit. What should I do with a book that is red watermarked! To browse Academia. Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Naji Ahmed.
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