## Dictionary of Analysis Calculus and Differential Equations

• Author : Douglas N. Clark
• Publisher : CRC Press
• Release Date : 1999-12-15
• Genre: Mathematics
• Pages : 294
• ISBN 10 : 1420049992

Dictionary of Analysis Calculus and Differential Equations Excerpt :

Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the occasional-if not frequent-need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Analysis, Calculus, and Differential Equations - the first published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,500 detailed definitions, written in a clear, readable style and complete with alternative meanings, and related references.

## Multivariable Calculus Linear Algebra and Differential Equations

• Author : Stanley I. Grossman
• Release Date : 2014-05-10
• Genre: Mathematics
• Pages : 992
• ISBN 10 : 9781483218038

Multivariable Calculus Linear Algebra and Differential Equations Excerpt :

Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

## Multivariable Mathematics

• Author : Richard E. Williamson
• Publisher : Pearson
• Release Date : 2004
• Genre: Mathematics
• Pages : 878
• ISBN 10 : UOM:39076002790512

Multivariable Mathematics Excerpt :

This book explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. Unique coverage including, the introduction of vector geometry and matrix algrebra, the early introduction of the gradient vector as the key to differentiability, optional numerical methods. For any reader interested in learning more about this discipline.

## Calculus

• Author : Gilbert Strang
• Publisher : Unknown
• Release Date : 2016-03-07
• Genre: Calculus
• Pages : 1026
• ISBN 10 : 1938168070

Calculus Excerpt :

"Calculus Volume 3 is the third of three volumes designed for the two- or three-semester calculus course. For many students, this course provides the foundation to a career in mathematics, science, or engineering."-- OpenStax, Rice University

## Differential Equations and the Calculus of Variations

• Author : Lev Ernestovich El?sgol?ts
• Publisher : Unknown
• Release Date : 1970
• Genre: Calculus of variations
• Pages : 440
• ISBN 10 : UOM:39015017329825

Differential Equations and the Calculus of Variations Excerpt :

## Vector Calculus and Differential Equations

• Author : Albert G. Fadell
• Publisher : Unknown
• Release Date : 1968
• Genre: Calculus
• Pages : 558
• ISBN 10 : LCCN:65001488

Vector Calculus and Differential Equations Excerpt :

## Calculus and Differential Equations with Mathematica

• Author : Pramote Dechaumphai
• Publisher : Alpha Science International, Limited
• Release Date : 2016-05-04
• Genre: Calculus
• Pages : 428
• ISBN 10 : 1783322640

Calculus and Differential Equations with Mathematica Excerpt :

Symbolic mathematics software have played an important role in learning calculus and differential equations. MATHEMATICA is one of the most powerful software being used to solve various types of problems in mathematics. This book presents a clear and easy-to-understand on how to use MATHEMATICA to solve calculus and differential equation problems. The book contains essential topics that are taught in calculus and differential equation courses. These topics are the limits, differentiation, integration, series, ordinary differential equations, Laplace and Fourier transforms, as well as special functions normally encountered in solving science and engineering problems. Numerical methods, in addition, are employed when the exact solutions are not available. The finite element method developed in the latest MATHEMATICA version is used to analyse partial differential equations for problems with complex geometry. The partial differential equations could be in elliptic, parabolic and hyperbolic forms. A large number of examples are presented with detailed derivation for their solutions before using MATHEMATICA to confirm the same results. With the clear explanation of all topics in this book and with the help of MATHEMATICA software, students will enjoy learning calculus and differential equations as compared to the traditional way in the past.

## Ordinary Differential Equations and Calculus of Variations

• Author : M V Makarets
• Publisher : World Scientific
• Release Date : 1995-06-30
• Genre: Mathematics
• Pages : 384
• ISBN 10 : 9789814500760

Ordinary Differential Equations and Calculus of Variations Excerpt :

This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students — much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications. Contents:First Order Differential EquationsN-th Order Differential EquationsLinear Second Order EquationsSystems of Differential EquationsPartial Equations of the First OrderNonlinear Equations and StabilityCalculus of VariationsAnswers to Problems Readership: Mathematicians and engineers. keywords:Examples;Differential Equations;Calculus of Variations “… the book can be successfully used both by students and practising engineers.” Mathematics Abstracts

## Differential Equations From Calculus to Dynamical Systems Second Edition

• Author : Virginia W. Noonburg
• Publisher : American Mathematical Soc.
• Release Date : 2020-08-28
• Genre: Education
• Pages : 402
• ISBN 10 : 9781470463298

Differential Equations From Calculus to Dynamical Systems Second Edition Excerpt :

A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature.

Score: 5
From 1 Ratings

## Differential Equations and Vector Calculus

• Author : Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad
• Publisher : S. Chand Publishing
• Release Date : 2023-01-31
• Genre: Science
• Pages : null
• ISBN 10 : 9789352838264

Differential Equations and Vector Calculus Excerpt :

In this book, how to solve such type equations has been elaborately described. In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the

Score: 5
From 4 Ratings

• Author : Lynn Harold Loomis
• Publisher : World Scientific Publishing Company
• Release Date : 2014-02-26
• Genre: Mathematics
• Pages : 596
• ISBN 10 : 9789814583954

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

## Malliavin Calculus with Applications to Stochastic Partial Differential Equations

• Author : Marta Sanz-Sole
• Publisher : CRC Press
• Release Date : 2005-08-17
• Genre: Mathematics
• Pages : 150
• ISBN 10 : 1439818940

Malliavin Calculus with Applications to Stochastic Partial Differential Equations Excerpt :

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself based on a general Gaussian space, going from the simple, finite-dimensional setting to the infinite-dimensional one. The final three chapters discuss recent research on regularity of the solution of stochastic partial differential equations and the existence and smoothness of their probability laws. About the author: Marta Sanz-Solé is Professor at the Faculty of Mathematics, University of Barcelona. She is a leading member of the research group on stochastic analysis at Barcelona, and in 1998 she received the Narcis Monturiol Award of Scientific and Technological Excellence from the autonomous government of Catalonia.

## Calculus of Variations and Partial Differential Equations

• Author : Luigi Ambrosio
• Publisher : Springer Science & Business Media
• Release Date : 2012-12-06
• Genre: Mathematics
• Pages : 348
• ISBN 10 : 9783642571862

Calculus of Variations and Partial Differential Equations Excerpt :

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

## Calculus and Differential Equations with MATLAB

• Author : Pramote Dechaumphai
• Publisher : Unknown
• Release Date : 2016-06-30
• Genre: Mathematics
• Pages : 441
• ISBN 10 : 1783322659

Calculus and Differential Equations with MATLAB Excerpt :

Calculus and Differential Equations with MATLAB presents a clear, easy-to-understand on how to use MATLAB to solve calculus and differential equation problems. The book contains eleven chapters with essential materials that are taught in calculus and differential equation courses. These include: - Limits, differentiation and integration. - Taylor, maclaurin and other infinite series. - Ordinary differential equations. - Laplace and Fourier transforms. - Partial differential equations. - Numerical and finite element methods. - Special functions (error, gamma, beta, Bessel, Airy, Legendre, etc.). Exact solutions are derived before showing MATLAB commands to provide the same solutions. Numerical methods are used to obtain approximate solutions when exact solutions are not available. The book contains a large number of examples and homework problems to demonstrate the capability of symbolic mathematics in MATLAB for solving calculus and differential equation problems.

## Cohomological Analysis of Partial Differential Equations and Secondary Calculus

• Author : A. M. Vinogradov
• Publisher : American Mathematical Soc.
• Release Date : 2001-10-16
• Genre: Mathematics
• Pages : 268
• ISBN 10 : 0821897993

Cohomological Analysis of Partial Differential Equations and Secondary Calculus Excerpt :

This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory "in action".