Handbook of vector and polyadic analysis

Title Page......Page 1
Copyright Page......Page 2
Preface......Page 3
Contents......Page 5
Scalars vs. Vectors......Page 7
Notation......Page 9
Definitions and Elementary Operations......Page 11
Scalar Product......Page 13
Vector Product......Page 15
Position Vectors......Page 16
Linear Vector Functions of Vectors......Page 17
Dyadics, Tensors, and Linear Vector Operators......Page 20
Dyadic Representation of Linear Vector Operators......Page 23
Polydot Products of Polyads......Page 27
Unit Polyads......Page 28
Polyadics......Page 30
Transposes and Adjoints of Polyadics......Page 33
Idemfactors, Deviation Factors, Transposers, and related functions......Page 37
Linear Polyadic Functions of Polyadics......Page 51
Use of Linear Operators with Arguments of Various Ranks......Page 58
Polycross Products......Page 63
Versors: Rotation Operators......Page 64
Invariants of Vectors and Polyadics......Page 70
Differentiation with respect to Vectors and Polyadics......Page 75
The Divergence and Gauss's Theorem......Page 80
The Circulation, the Curl, Stokes Theorem......Page 81
Operations with V and dW......Page 84
Mixed Derivative Operators......Page 88
Maclaurin's and Taylor's Series......Page 89
Appendix A: Summary of Formulas and Notation......Page 91
Appendix B : Ternary Numeration......Page 102
Appendix C : Comparison of Notation......Page 104
Appendix D: Miscellaneous Exercises......Page 105
References on Vector Analysis......Page 109