Description
DOVER PUBLICATIONS Rational Quadratic Forms 2008 Edition by CASSELS J. W. S.
This exploration of quadratic forms over rational numbers and rational integers offers an excellent elementary introduction to many aspects of a classical subject, including recent developments. The author, a Professor Emeritus at Trinity College, University of Cambridge, offers a largely self-contained treatment that develops most of the prerequisites.Topics include the theory of quadratic forms over local fields, forms with integral coefficients, genera and spinor genera, reduction theory for definite forms, and Gauss' composition theory. The final chapter explains how to formulate the proofs in earlier chapters independently of Dirichlet's theorems related to the existence of primes in arithmetic progressions. Specialists will particularly value the several helpful appendixes on class numbers, Siegel's formulas, Tamagawa numbers, and other topics. Each chapter concludes with many exercises and hints, plus notes that include historical remarks and references to the literature. Preface1. Introduction2. General Equations of Motion and the Representation of Non-linearities3. Probability Theory and Stochastic Processes4. Elements of Linear Random Vibration Theory5. Statistical Linearization for Simple Systems with Stationary Response6. Statistical Linearization of Multi-Degree of Freedom Systems with Stationary Response7. Non-stationary Problems8. Systems with Hysteretic Non-linearity9. Relaxation of the Gaussian Response Assumption10. Accuracy of Statistical LinearizationAppendixes. References. Author Index. Subject Index