Advanced Calculus Partial Differential Equations
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Advanced Calculus Partial Differential Equations
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Author : B.R. THAKUR
language : en
Publisher: Ram Prasad Publications(R.P.H.)
Release Date :
Advanced Calculus Partial Differential Equations written by B.R. THAKUR and has been published by Ram Prasad Publications(R.P.H.) this book supported file pdf, txt, epub, kindle and other format this book has been release on with Juvenile Fiction categories.
–Unit-I– 1.1 Historical background : 1.1.1 A brief historical background of Calculus and partial differential equations in the context of India and Indian heritage and culture 1.1.2 Abrief biography of Bodhayana 1.2 Field structure and ordered structure of R, Intervals, Bounded and Unbounded sets, Supremum and Infimum, Completeness in R, Absolute value of a real number. 1.3 Sequence of real numbers 1.4 Limit of a sequence 1.5 Bounded and Monotonic sequences 1.6 Cauchy’s general principle of convergence 1.7 Algebra of sequence and some important theorems –Unit-II– 2.1 Series of non-negative terms 2.2 Convergence of positive term series 2.3 Alternating series and Leibnitz’s test 2.4 Absolute and Conditional Convergence of Series of real terms 2.5 Uniform continuity 2.6 Chain rule of differentiability 2.7 Mean value theorems and their geometrical interpretations –Unit-III– 3.1 Limit and Continuity of functions of two variables 3.2 Change of variables 3.3 Euler’s theorem on homogeneous functions 3.4 Taylor’s theorem for function of two variables 3.5 Jacobians 3.6 Maxima and Minima of functions of two variables 3.7 Lagrange’s multiplier method 3.8 Beta and Gamma Functions –Unit-IV– 4.1 Partial differential equations of the first order 4.2 Lagrange’s solution 4.3 Some special types of equations which can be solved easily by methods other than the general method 4.4 Charpit’s general method 4.5 Partial differential equations of second and higher orders –Unit-V– 5.1 Classification of partial differential equations of second order 5.2 Homogeneous and non-homogeneous partial differential equations of constant coefficients 5.3 Partial differential equations reducible to equations with constant coefficients
Advanced Calculus For Applications
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Author : Francis Begnaud Hildebrand
language : en
Publisher: Prentice Hall
Release Date : 1976
Advanced Calculus For Applications written by Francis Begnaud Hildebrand and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
The text provides advanced undergraduates with the necessary background in advanced calculus topics, providing the foundation for partial differential equations and analysis. Readers of this text should be well-prepared to study from graduate-level texts and publications of similar level. KEY TOPICS: Ordinary Differential Equations; The Laplace Transform; Numerical Methods for Solving Ordinary Differential Equations; Series Solutions of Differential Equations: Special Functions; Boundary-Value Problems and Characteristic-Function Representations; Vector Analysis; Topics in Higher-Dimensional Calculus; Partial Differential Equations; Solutions of Partial Differential Equations of Mathematical Physics; Functions of a Complex Variable; Applications of Analytic Function Theory MARKET: For all readers interested in advanced calculus.
Advanced Calculus
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Author : Wilfred Kaplan
language : en
Publisher: Tata McGraw-Hill Education
Release Date : 1952
Advanced Calculus written by Wilfred Kaplan and has been published by Tata McGraw-Hill Education this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Calculo categories.
Advanced Calculus For Applications
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Author : Francis B. Hildebrand
language : en
Publisher:
Release Date : 2003-01
Advanced Calculus For Applications written by Francis B. Hildebrand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01 with categories.
Partial Differential Equations
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Author : Rustum Choksi
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-04
Partial Differential Equations written by Rustum Choksi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-04 with Mathematics categories.
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment. The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
Partial Differential Equations I
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Author : Michael E. Taylor
language : en
Publisher: Springer Nature
Release Date : 2023-12-06
Partial Differential Equations I written by Michael E. Taylor and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-06 with Mathematics categories.
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)
Advanced Calculus
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Author : Tomá¿ Kisela
language : en
Publisher:
Release Date : 2018-06
Advanced Calculus written by Tomá¿ Kisela and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06 with categories.
Calculus is a very multipurpose and valuable tool. It is one of the greatest inventions of modern science. There is just so much it can offer. The success of calculus has been extended over time into various other important topics in mathematics. Some are: differential equations, vector calculus, calculus of variations, complex analysis and differential topology. Calculus is intensely integrated in every branch of the physical sciences, such as physics and biology. It is found in computer science, statistics, and engineering; in economics, business, and medicine. Modern developments such as architecture, aviation, and other technologies all make use of what calculus can offer. This book "Advanced Calculus" is intended to present coverage on harmonic analysis, integral transforms and equations, ordinary and partial differential equations, measure and integration, sequences and series, functional analysis, functions of real and complex variables, approximation and expansions. It gives an exposition of methods for approximating integrals, including those that are multidimensional. Applications of some of these methods in statistics are discussed. This subject area has recently gained prominence in several fields of science and engineering, and, in particular, Bayesian statistics. The material should be helpful to readers who may be interested in pursuing further studies in this area. Advanced calculus has had a fundamental and seminal role in the development of the basic theory underlying statistical methodology. With the rapid growth of statistics as a discipline, particularly in the last three decades, knowledge of advanced calculus has become imperative for understanding the recent advances in this field. Students as well as research workers in statistics are expected to have a certain level of mathematical sophistication in order to cope with the intricacies necessitated by the emerging of new statistical methodologies. This book is unique also in its special attention to the needs of applications and due to its unusually elaborate motivations coming from the history of mathematics and applications. This book is designed for advanced graduate students, practitioners as well as for those who are novice researchers in this field.
Introduction To Partial Differential Equations And Hilbert Space Methods
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Author : Karl E. Gustafson
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Introduction To Partial Differential Equations And Hilbert Space Methods written by Karl E. Gustafson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Mathematical Physics With Partial Differential Equations
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Author : James Kirkwood
language : en
Publisher: Academic Press
Release Date : 2018-02-26
Mathematical Physics With Partial Differential Equations written by James Kirkwood and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-26 with Mathematics categories.
Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace's equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green's functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods. - Introduces and evaluates numerous physical and engineering concepts in a rigorous mathematical framework - Provides extremely detailed mathematical derivations and solutions with extensive proofs and weighting for application potential - Explores an array of detailed examples from physics that give direct application to rigorous mathematics - Offers instructors useful resources for teaching, including an illustrated instructor's manual, PowerPoint presentations in each chapter and a solutions manual
Invitation To Partial Differential Equations
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Author : Mikhail Shubin
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-08
Invitation To Partial Differential Equations written by Mikhail Shubin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.
This book is based on notes from a beginning graduate course on partial differential equations. Prerequisites for using the book are a solid undergraduate course in real analysis. There are more than 100 exercises in the book. Some of them are just exercises, whereas others, even though they may require new ideas to solve them, provide additional important information about the subject. It is a great pleasure to see this book—written by a great master of the subject—finally in print. This treatment of a core part of mathematics and its applications offers the student both a solid foundation in basic calculations techniques in the subject, as well as a basic introduction to the more general machinery, e.g., distributions, Sobolev spaces, etc., which are such a key part of any modern treatment. As such this book is ideal for more advanced undergraduates as well as mathematically inclined students from engineering or the natural sciences. Shubin has a lovely intuitive writing style which provides a gentle introduction to this beautiful subject. Many good exercises (and solutions) are provided! —Rafe Mazzeo, Stanford University This text provides an excellent semester's introduction to classical and modern topics in linear PDE, suitable for students with a background in advanced calculus and Lebesgue integration. The author intersperses treatments of the Laplace, heat, and wave equations with developments of various functional analytic tools, particularly distribution theory and spectral theory, introducing key concepts while deftly avoiding heavy technicalities. —Michael Taylor, University of North Carolina, Chapel Hill