Solving Higher-Order Equations
Solving Higher-Order Equations

Author: Christian Prehofer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 193

ISBN-13: 1461217784

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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.

Notes on Diffy Qs
Notes on Diffy Qs

Author: Jiri Lebl

Publisher:

Published: 2019-11-13

Total Pages: 468

ISBN-13: 9781706230236

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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.

Elementary Differential Equations with Boundary Value Problems
Elementary Differential Equations with Boundary Value Problems

Author: William F. Trench

Publisher: Thomson Brooks/Cole

Published: 2001

Total Pages: 764

ISBN-13:

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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.

Differential Equations
Differential Equations

Author: Clay C. Ross

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 445

ISBN-13: 1475739494

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The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.

Solving Systems of Polynomial Equations
Solving Systems of Polynomial Equations

Author: Bernd Sturmfels

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 162

ISBN-13: 0821832514

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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics

Author: Dennis Zill

Publisher: Jones & Bartlett Learning

Published: 2011

Total Pages: 1005

ISBN-13: 0763779660

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Accompanying CD-ROM contains ... "a chapter on engineering statistics and probability / by N. Bali, M. Goyal, and C. Watkins."--CD-ROM label.

Mathematics for the Physical Sciences
Mathematics for the Physical Sciences

Author: Herbert S Wilf

Publisher: Courier Corporation

Published: 2013-01-18

Total Pages: 304

ISBN-13: 0486153347

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Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.

Higher-Order Numerical Methods for Transient Wave Equations
Higher-Order Numerical Methods for Transient Wave Equations

Author: Gary Cohen

Publisher: Springer Science & Business Media

Published: 2001-11-06

Total Pages: 372

ISBN-13: 9783540415985

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"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

Partial Differential Equations
Partial Differential Equations

Author: Walter A. Strauss

Publisher: John Wiley & Sons

Published: 2007-12-21

Total Pages: 467

ISBN-13: 0470054565

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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.