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Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.

7. 2 Element Stiffness Matrix of a Space Truss Local Coordinates 221 7. 3 Transformation of the Element Stiffness Matrix 223 7. 4 Element Axial Force 224 7. 5 Assemblage ofthe System Stiffness Matrix 225 7. 6 Problems 236 8 STATIC CONDENSATION AND SUBSTRUCTURING 8. 1 Introduction 239 8. 2 Static Condensation 239 8. 3 Substructuring 244 8. 4 Problems 259 9 INTRODUCTION TO FINITE ELEMENT MEmOD 9. 1 Introduction 261 9. 2 Plane Elasticity Problems 262 9. 3 Plate Bending 285 9. 4 Rectangular Finite Element for Plate Bending 285 9. 5 Problems 298 APPENDIX I Equivalent Nodal Forces 301 APPENDIXll Displacement Functions for Fixed-End Beams 305 GLOSSARY 309 SELECTED BmLIOGRAPHY 317 INDEX 319 ix Preface This is the first volume of a series of integrated textbooks for the analysis and design of structures. The series is projected to include a first volume in Matrix Structural Analysis to be followed by volumes in Structural Dynamics and Earthquake Engineering as well as other volumes dealing with specialized or advanced topics in the analysis and design of structures. An important objective in the preparation of these volumes is to integrate and unify the presentation using common notation, symbols and general format. Furthermore, all of these volumes will be using the same structural computer program, SAP2000, developed and maintained by Computers and Structures, Inc. , Berkeley, California.

Broadband opamps for multi-channel communication systems make strong demands on linearity performance. This book, written for Analog CMOS designers, presents a thorough analysis of the nonlinear behaviour of circuits, to obtain opamps with low distortion.