<p>The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.<br>Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary differential equations. The authors offer a coherent treatment of the fundamental concepts of Lie group theory, and they present a proof of the basic theorem relating Lie subalgebras to Lie subgroups. Additional topics include fiber bundles and multilinear algebra. An excellent source of examples and exercises, this graduate-level text requires a solid understanding of the basic theory of finite-dimensional vector spaces and their linear transformations, point-set topology, and advanced calculus.  </p>

Introduction to Differentiable Manifolds (Dover Books on Mathematics)

Science & Math

Louis Auslander

Robert E. MacKenzie

Mathematics

Dover Publications

Mathematics through statistics

Williams & Wilkins Co.

Signal Processing: Signal Processing Theory Pt. 1

Engineering & Transportation

Engineering

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

These two volumes of Signal Processing are based on lectures delivered during a six week program held at the Institute for Mathematics and Its Applications, Minneapolis, MN. The first two weeks of the program dealt with general areas and methods of Signal Processing. The problem areas included imaging and analysis of recognition, x-ray crystallography, radar and sonar, signal analysis and 1-D signal processing, speech, vision, and VLSI implementation. The methods discussed included harmonic analysis and wavelets, operator theory, algorithm complexity, filtering and estimation, and inverse scattering. The topics of weeks three and four were digital filter, VLSI implementation, and integrable circuit modelling. In week five the concentration was on robust and nonlinear control with aerospace applications, and in week six emphasis was on problems in radar, sonar and medical imaging. Because of the large overlap between the various one-week and two-week segments of the program, the material has been divided into two parts. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes.  These two volumes will serve as a source of information and stimulation to mathematical scientists who wish to get acquainted with signal processing.

Signal processing (The IMA volumes in mathematics and its applications)

Springer, Verlag

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Books by Louis Auslander