Differential Equations And Vector Calculus

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Differential Equations And Vector Calculus

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Author : Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad
language : en
Publisher: S. Chand Publishing
Release Date :

Differential Equations And Vector Calculus written by Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.

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

Multivariable Calculus Linear Algebra And Differential Equations

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Author : Stanley I. Grossman
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Multivariable Calculus Linear Algebra And Differential Equations written by Stanley I. Grossman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

Differential Equations And Vector Calculus

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Author : Dr. Bhimanand Pandurang Gajbhare , Dr. A.Rushi Kesava , Dr. K.Rajanikanth , Dr. V. T. Hosamath
language : en
Publisher: RK Publication
Release Date : 2025-04-03

Differential Equations And Vector Calculus written by Dr. Bhimanand Pandurang Gajbhare , Dr. A.Rushi Kesava , Dr. K.Rajanikanth , Dr. V. T. Hosamath and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-03 with Mathematics categories.

Differential Equations and Vector Calculus explores the mathematical foundations essential for physics and engineering. Covering ordinary differential equations, partial differential equations, and vector calculus topics like gradient, divergence, and curl, it provides theoretical insights and practical problem-solving techniques. Ideal for undergraduate students in science, mathematics, and engineering disciplines.

Tensor And Vector Analysis

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Author : C. E. Springer
language : en
Publisher: Courier Corporation
Release Date : 2013-09-26

Tensor And Vector Analysis written by C. E. Springer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Vector Calculus And Linear Algebra

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Author : Oliver Knill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-04-30

Vector Calculus And Linear Algebra written by Oliver Knill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-30 with Mathematics categories.

This book covers vector calculus up to the integral theorems; linear algebra up to the spectral theorem; and harmonic analysis until the Dirichlet theorem on convergence of Fourier series with applications to partial differential equations. It also contains a unique introduction to proofs, while providing a solid foundation in understanding the proof techniques better.The book incorporates fundamentals from advanced calculus and linear algebra but it is still accessible to a rather general student audience.Students will find materials that are usually left out like differential forms in calculus, the Taylor theorem in arbitrary dimensions or the Jordan normal form in linear algebra, the convergence proof of Fourier series, and how to do calculus on discrete networks.The contents of this book were used to teach in a two-semester course at Harvard University during fall 2018 and spring 2019. For the last 30 years, Oliver Knill has taught calculus, linear algebra, probability theory and differential equations starting at ETH Zürich, moving onward to Caltech, and the University of Arizona, and ever since 2000, at Harvard.

Vector Calculus And Differential Equations

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Author :
language : en
Publisher:
Release Date : 1968

Vector Calculus And Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Calculus categories.

Applications Of Vector Analysis And Complex Variables In Engineering

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Author : Otto D. L. Strack
language : en
Publisher: Springer Nature
Release Date : 2020-04-18

Applications Of Vector Analysis And Complex Variables In Engineering written by Otto D. L. Strack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-18 with Technology & Engineering categories.

This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.

A History Of Vector Analysis

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Author : Michael J. Crowe
language : en
Publisher: Courier Corporation
Release Date : 1994-01-01

A History Of Vector Analysis written by Michael J. Crowe and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Vector Valued Partial Differential Equations And Applications

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Author : Bernard Dacorogna
language : en
Publisher: Springer
Release Date : 2017-05-29

Vector Valued Partial Differential Equations And Applications written by Bernard Dacorogna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Mathematics categories.

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Vector Calculus

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Author : Paul C. Matthews
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Vector Calculus written by Paul C. Matthews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.