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The Resource A Course of Higher Mathematics : International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1

A Course of Higher Mathematics : International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1

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A Course of Higher Mathematics : International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1
Title
A Course of Higher Mathematics
Title remainder
International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1
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eng
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A Course of Higher Mathematics : International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1
Label
A Course of Higher Mathematics : International Series of Monographs In: Pure and Applied Mathematics, Volume 3P1
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online resource
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multicolored
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text
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txt
Content type MARC source
rdacontent
Contents
  • Front Cover -- A Course of Higher Mathematics -- Copyright Page -- Table of Contents -- INTRODUCTION -- PREFACE TO THE FOURTH RUSSIAN EDITION -- CHAPTER I . DETERMINANTS. THE SOLUTION OF SYSTEMS OF EQUATIONS -- 1· Properties of determinants -- 2. The solution of systems of equations -- CHAPTER II. LINEAR TRANSFORMATIONS AND QUADRATIC FORMS -- 20. Coordinate transformations in three-dimensional space. -- 21· General linear transformations of real three-dimensional space. -- 22. Covariant and contravariant affine vectors. -- 23. Tensors. -- 24. Examples of affine orthogonal tensors. -- 25· The case of n-dimeneional complex space· -- 26. Basic matrix calculus. -- 27· Characteristic roots of matrices and reduction to canonical form· -- 28. Unitary and orthogonal transformations. -- 29. Buniakowski's inequality. -- 30· Properties of scalar products and norms. -- 31. Orthogonalization of vectors. -- 32· Transformation of a quadratic form to a sum of squares· -- 33. The case of multiple roots of the characteristic equation. -- 34. Examples. -- 35. Classification of quadratic forms. -- 36. Jacobi's formula. -- 37. The simultaneous reduction of two quadratic forms to sums of squares. -- 38. Small vibrations. -- 39. Extremal properties of the eigenvalues of quadratic forms. -- 40. Hermitian matrices and Hermitian forms. -- 41. Commutative Hermitian matrices· -- 42. The reduction of unitary matrices to the diagonal form. -- 43. Projection matrices. -- 44. Functions of matrices. -- 45· Infinite-dimensional space. -- 46. The convergence of vectors. -- 47. Complete systems of mutually orthogonal vectors. -- 48. Linear transformations with an infinite set of variables. -- 49. Functional space. -- 50. The connection between functional and Hilbert space. -- 51. Linear functional operators
  • CHAPTER III. THE BASIC THEORY OF GROUPS AND LINEAR REPRESENTATIONS OF GROUPS -- 52. Groups of linear transformations. -- 53. Groups of regular polyhedra. -- 54. Lorentz transformations. -- 55. Permutations· -- 56. Abstract groups. -- 57. Subgroups· -- 58. Classes and normal subgroups. -- 59. Examples. -- 60. Isomorphic and homomorphic groups. -- 61. Examples. -- 62. Stereographic projections· -- 63· Unitary groups and groups of rotations· -- 64. The general linear group and the Lorentz group. -- 65· Representation of a group by linear transformations. -- 66. Basic theorems. -- 67. Abelian groups and representations of the first degree. -- 68· Linear representations of the unitary group in two variables. -- 69. Linear representations of the rotation group· -- 70. The theorem on the simplicity of the rotation group· -- 71. Laplace's equation and linear representations of the rotation group. -- 72. Direct matrix products. -- 73. The composition of two linear representations of a group· -- 74. The direct product of groups and its linear representations. -- 75· Decomposition of the composition Dj X Dy of linear representations of the rotation group· -- 76. Orthogonality. -- 77. Characters. -- 78. Regular representations of groups. -- 79. Examples of representations of finite groups. -- 80. Representations of a linear group in two variables. -- 81. Theorem on the simplicity of the Lorentz group· -- 82. Continuous groups· Structural constants. -- 83. Infinitesimal transformations. -- 84. Rotation groups. -- 85. Infinitesimal transformations and representations of the rotation group· -- 86. Representations of the Lorentz group· -- 87. Auxiliary formulae. -- 88. The formation of groups with given structural constants. -- 89. Integration over groups. -- 90. Orthogonality. Examples. -- INDEX -- VOLUMES PUBLISHED IN THIS SERIES
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