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Klappentext Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress! strain! and other tensor quantities! so that they can follow! and apply to their own research! developments in modern! quantitative geology. This book! based on a course taught by the author at UCLA! can provide the proper introduction. Included throughout the eight chapters are 136 complex problems! advancing from vector algebra in standard and subscript notations! to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help! students can monitor their progress! and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations. Zusammenfassung This book of problem sets and answers, based on notes for a graduate course in structural geology at UCLA, is a review of the mathematics of vectors and of stress and strain, including finite strain. The main purpose of the problem sets is to "Illuminate branches of physics pertinent to geology, including structural geology, glaciology, crystallography, crystal physics, the geophysics of heat flow and others." Students of geology who have only a modest background in mathematics may wish to become familiar with theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. A set of 136 progressively more complex problems is introduced in eight chapters, which advance from vector algebra in standard and subscript notations to the mathematical description of finite strain and its compounding and decomposition. A complete set of fully worked solutions for the problems makes up the largest part of the book. With its help, students, guided by an instructor or self-taught, can avoid pitfalls and monitor their progress. Eventually, geologists who have worked their way through these problems should be able to confidently use the subscript and matrix notations and to formulate and solve tensor problems on their own....
Sommario
- 1: Vectors
- 2: Fields
- 3: Matter Tensors and Coordinate Transformations
- 4: Stress
- 5: Infinitesimal Strain and Rotation
- 6: Finite Strain
- 7: Effects of Stress
- 8: Strain History and Polar Deomposition
- 9: Summary of Formulae
