Solving Higher Order Equations
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| Author | : Christian Prehofer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 193 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461217784 |
This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.
| Author | : Jiri Lebl |
| Publisher | : |
| Total Pages | : 468 |
| Release | : 2019-11-13 |
| Genre | : |
| ISBN | : 9781706230236 |
Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.
| Author | : William F. Trench |
| Publisher | : Thomson Brooks/Cole |
| Total Pages | : 764 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Dennis Zill |
| Publisher | : Jones & Bartlett Learning |
| Total Pages | : 1005 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0763779660 |
Accompanying CD-ROM contains ... "a chapter on engineering statistics and probability / by N. Bali, M. Goyal, and C. Watkins."--CD-ROM label.
| Author | : Bernd Sturmfels |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821832514 |
Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
| Author | : Ravi P Agarwal |
| Publisher | : World Scientific |
| Total Pages | : 321 |
| Release | : 1986-07-01 |
| Genre | : Mathematics |
| ISBN | : 9814513636 |
Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems
| Author | : Alicia Dickenstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2005-04-27 |
| Genre | : Computers |
| ISBN | : 3540243267 |
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
| Author | : Christian Prehofer |
| Publisher | : |
| Total Pages | : 186 |
| Release | : 1998 |
| Genre | : Computer logic |
| ISBN | : 9783764340322 |
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
| Author | : Gary Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 372 |
| Release | : 2001-11-06 |
| Genre | : Science |
| ISBN | : 9783540415985 |
"To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003
