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Calculus with Curvilinear Coordinates
This book presents problems and solutions in calculus with curvilinear coordinates. Vector analysis can be performed in different coordinate systems, an optimal system considers the symmetry of the problem in order to reduce calculatory difficulty. The book presents the material in arbitrary orthogonal coordinates, and includes the discussion of parametrization methods as well as topics such as potential theory and integral theorems. The target audience primarily comprises university teachers in engineering mathematics, but the book may also be beneficial for advanced undergraduate and graduate students alike.
The Fundamentals of Mathematical Analysis
The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed m...
Flux Coordinates and Magnetic Field Structure
Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.
Mathematical Methods for Engineers and Scientists 2
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems
This book describes analytical methods for modelling drop evaporation, providing the mathematical tools needed in order to generalise transport and constitutive equations and to find analytical solutions in curvilinear coordinate systems. Transport phenomena in gas mixtures are treated in considerable detail, and the basics of differential geometry are introduced in order to describe interface-related transport phenomena. One chapter is solely devoted to the description of sixteen different orthogonal curvilinear coordinate systems, reporting explicitly on the forms of their differential operators (gradient, divergent, curl, Laplacian) and transformation matrices. The book is intended to guide the reader from mathematics, to physical descriptions, and ultimately to engineering applications, in order to demonstrate the effectiveness of applied mathematics when properly adapted to the real world. Though the book primarily addresses the needs of engineering researchers, it will also benefit graduate students.
Vector Calculus
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 r...
Lectures on Classical Differential Geometry
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conc...
Modeling Thermodynamic Distance, Curvature and Fluctuations
This textbook aims to briefly outline the main directions in which the geometrization of thermodynamics has been developed in the last decades. The textbook is accessible to people trained in thermal sciences but not necessarily with solid formation in mathematics. For this, in the first chapters a summary of the main mathematical concepts is made. In some sense, this makes the textbook self-consistent. The rest of the textbook consists of a collection of results previously obtained in this young branch of thermodynamics. The manner of presentation used throughout the textbook is adapted for ease of access of readers with education in natural and technical sciences.
Theoretical Computational Dynamics
Emphasis of this text is on the basic assumptions and the formulation of the theory of compressible flow as well as on the methods of solving problems. Published by Science Press, Beijing, distributed by VNR in the US. Annotation copyrighted by Book News, Inc., Portland, OR
