Page 7 - Textos de Matemática Vol. 42
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Contents
Preface ................................... vii
1 Introduction 1
2 Quaternions 3
2.1 Definition,algebraicproperties ................... 3
2.2 Rotationsinthreeandfourdimensions. . . . . . . . . . . . . . . 4
2.3 Various interpretations of the space H of quaternions . . . . . . . 6
2.4 Equivariantmultiplications ..................... 8
3 Quaternionic differential forms 9
3.1 TheGrassmannalgebraofR4 withvaluesinH . . . . . . . . . . 10 3.2 Thedecompositionofone-forms................... 11 3.3 Thedecompositionoftwo-forms .................. 14 3.4 Thedecompositionofthree-forms.................. 18 3.5 Quaternionic-valuedforms...................... 19
4 Monogenic functions of quaternionic variable 21
4.1 Differentiablefunctions........................ 21 4.2 TheFueterequation ......................... 24 4.3 Some simple properties of monogenic functions . . . . . . . . . . 27 4.4 TheFueterconstruction ....................... 28 4.5 Conformalinvariance......................... 31 4.6 Examples ............................... 32
5 Cauchy integral formula 35
5.1 Cauchytheorem ........................... 35 5.2 Cauchyintegralformula ....................... 36
6 Residues 37
6.1 Homogeneousmonogenicfunctions ................. 37 6.2 Taylorseries.............................. 42 6.3 Laurentseries............................. 43
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