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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area
Reprint of the original, first published in 1903.
A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.