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Crystals, X-rays and ProteinsComprehensive Protein Crystallography$
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Dennis Sherwood and Jon Cooper

Print publication date: 2010

Print ISBN-13: 9780199559046

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199559046.001.0001

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Vector analysis and complex algebra

Vector analysis and complex algebra

(p.23) 2 Vector analysis and complex algebra
Crystals, X-rays and Proteins

Dennis Sherwood

Jon Cooper

Oxford University Press

This chapter introduces the essential mathematics of diffraction. Initially the concept of a vector is presented along with the mathematical operations which we can perform on vector quantities including addition, subtraction, and multiplication by a scalar. The important methods for multiplying two or more vector quantities (scalar or dot product and the vector or cross product) are then covered. Next the chapter describes the concept of complex numbers and their graphical representation in the form of an Argand diagram. Mathematical operations such as addition and multiplication of complex numbers are then covered, followed by the concepts of the complex conjugate and the complex exponential — both of utmost importance in understanding the mathematics of diffraction. The chapter then introduces briefly some of the mathematics of determinants.

Keywords:   vectors, vector operations, unit vectors, components, scalar product, vector product, triple product, complex numbers, Argand diagram, phase

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