Coordinate Transformation

Intended for a first-year graduate course in heat transfer, including topics relevant to aerospace engineering and chemical and nuclear engineering, this hardcover book deals systematically and comprehensively with modern mathematical methods of solving problems in heat conduction and diffusion. Chapter One offers exceptionally precise coverage of heat flux as a vector, derivation of the conduction equations, integral-transform technique and coordinate transformations. Chapter Two through Four deal with problem characteristics peculiar to cartesian, cylindrical and spherical coordinates. Chapter Five discusses the application of Duhamel's method and a comparison with the integral-transform technique, including the use of Green's function in solving boundary-value problems. Chapter Six covers the solution of heat-conduction problems in one-dimensional composite slabs, cylinders and spheres. Chapter Seven discusses the integral method of solution of nonlinear conduction problems involving temperature-dependent thermal properties, a change of phase and irregular geometries. Chapter Eight applies a number of useful transformations in the solution of nonlinear boundary value problems of heat conduction. Chapter Nine introduces numerical techniques such as the finite differences and the Monte-Carlo method. Chapter Ten treats anisotropic solids using the resistivity and conductivity tensors. Each chapter includes illustrative examples and problems, and there are a number of helpful appendices that will prove handy in solving problems. Selected references at the end of each chapter and a carefully prepared index further enhance the value of this volume as a textbook and a practical reference.Unabridged, corrected Dover republication of the edition published by the International Textbook Company, Scranton, Pa., 1968. Preface. Problems. Appendices. 134 line illustrations.

"Nothing comparable to it."--"Mathematics Teacher This comprehensive three-part treatment begins with a consideration of the simplest geometric manifolds: line-segment, area, and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of space according to their behavior under transformation of rectangular coordinates; and derivative manifolds. The second section, on geometric transformations, examines affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations. 1939 ed. 141 figures.

Active and passive transformation - In the physical sciences, an active transformation is one which actually changes the physical state of a system and makes sense even in the absence of a coordinate system whereas a passive transformation is merely a change in the coordinate system of no physical significance. The distinction between active and passive transformations is one which should always be kept in mind when working with transformations.

Coordinate rotation - In linear algebra and geometry, a coordinate rotation is a type of transformation from one system of coordinates to another system of coordinates such that distance between any two points remains invariant under the transformation. In other words, a rotation is a type of isometry â€“ note however that there are isometries other than rotations, such as translations, reflections, and glide reflections.

Galilean transformation - The Galilean transformation is used to transform between the coordinates of two coordinate systems in a constant relative motion in Newtonian physics. This is the passive transformation point of view.

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