Title : Higher Algebra
Format : Hardcover
Pages : 608 pages
Publisher : S. Barnard
Language : English
ISBN : 9781443730860

HIGHER ALGEBRA by S BARNARD First published in 1936 Contents include ix CHAPTER EXERCISE XV 128 Minors Expansion in Terms of Second Minors 132 133 Product of Two Iteterminants 134 Rectangular Arrays 135 Reciprocal Deteyrrtlilnts Two Methods of Expansion 136 137 Use of Double Suffix Symmetric and Skew symmetric Determinants Pfaffian 138 143 EXERCISE XVI 143 X SYSTEMS OF EUATIONS Definitions Euivalent Systems 149 150 Linear Euations in Two Unknowns Line at Infinity 150 152 Linear Euations in Three Unknowns Euation to a Plane Plane at Infinity 153 157 EXERCISE XVII 158 Systems of Euations of any Degree Methods of Solution for Special Types 160 164 EXERCISE XVIII 164 XL RECIPROCAL AND BINOMIAL EUATIONS Reduction of Reciprocal Euations 168 170 The Euation x n 1 0 Special Roots 170 171 The Euation x n A 0 172 The Euation a 17 1 0 Regular 17 sided Polygon 173 176 EXERCISE XIX 177 AND BIUADRATIC EUATIONS The Cubic Euation roots a jS y Euation whose Roots are y 2 etc Value of J Character of Roots 179 180 Cardan's Solution Trigonometrical Solution the Functions a f eo f V a f a 2 4 a y 180 181 Cubic as Sum of Two Cubes the Hessftfh 182 183 Tschirnhausen's Transformation 186 EXERCISE XX 184 The Biuadratic Euation roots a y 8 186 The Functions A y aS etc the Functions J J Reducing Cubic Character of Roots 187 189 Ferrari's Solution and Deductions 189 191 Descartes' Solution 191 Conditions for Four Real Roots 192 ty Transformation into Reciprocal Form 194 Tschirnhausen's Trans formation 195 EXERCISE XXI 197 OP IRRATIONALS Sections of the System of Rationals Dedekind's Definition 200 201 Euality and Ineuality 202 Use of Seuences in defining a Real Number Endless Decimals 203 204 The Fundamental Operations of Arithmetic Powers Roots and Surds 204 209 Irrational Indices Logarithms 209 210 Definitions Interval Steadily Increasing Functions 210 Sections of the System of DEGREES Real Numbers the Continuum 211 212 Ratio and Proportion Euclid's Definition 212 213 EXERCISE XXII 214 x CONTENTS CHAPTER XIV INEUALITIES Weierstrass' Ineualities 216 Elementary Methods 210 217 For n Numbers a l9 a 2 a JACJJ n n n a a I 219 xa x l a b a x b x DEGREES xb x l a 6 219 l x n DEGREES l nx 220 Arithmetic and Geometric Means 221 222 V DEGREES n and Extension 223 Maxima and Minima 223 224 EXERCISE XXIII 224 XV SEUENCES AND LIMITS Definitions Theorems Monotone Seuences 228 232 E ponential Ineualities and Limits l m i n l m 1 n 1 and 1 n m n mj nj 1 n l w lim 1 f lim l e 232233 n 00 V nj nj EXERCISE XXIV 233 General Principle of Convergence 235 237 Bounds of a Seuent Limits of Inde termination 237 240 Theorems 1 Increasing Seuence u n where u n u n DEGREES l 0 and u n l lu n l then u n n L 3 If lim u n l then lim U