A Treatise on the Calculus of Finite Differences (Cambridge Library Collection - Mathematics)

Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking. Cover......Page 1 A Treatise on the Calculus of Finite Differences......Page 4 Preface......Page 10 Contents......Page 12 CHAPTER I - NATURE OF THE CALCULUS OF FINITE DIFFERENCES......Page 14 CHAPTER II - DIRECT THEOREMS OF FINITE DIFFERENCES......Page 17 Nature of the Problem......Page 41 Given values equidistant......Page 42 Not equidistant......Page 46 Application of Lagrange's Theorem......Page 48 Areas of Curves......Page 49 Application to Statistics......Page 54 Exercises......Page 57 Meaning of Integration......Page 58 Periodical Constants......Page 60 Integrable Forms......Page 61 Summation of Series......Page 69 Connexion of Methods......Page 72 Conditions of extension of direct to inverse forms......Page 74 Exercises......Page 76 Definitions......Page 78 Fundamental Proposition......Page 79 First derived Criterion......Page 82 Supplemental Criteria......Page 84 Exercises......Page 92 Development of [GREEK CAPITAL LETTER SIGMA]ux,......Page 93 Bernoulli's Numbers......Page 96 Applications......Page 97 Limits of the Series for [GREEK CAPITAL LETTER SIGMA]ux......Page 104 Other forms of [GREEK CAPITAL LETTER SIGMA]ux......Page 107 Exercises......Page 110 Genesis......Page 112 Linear Equations of the first orders......Page 114 Linear Equations with constant Coefficients......Page 119 Symbolical Solution......Page 120 Equations reducible to Linear Equations with constant Coefficients......Page 127 Analogy with Differential Equations......Page 131 Fundamental Connexion with Differential Equations......Page 134 Exercises......Page 136 Theory of these Equations......Page 138 Solutions derived from the Variation of a Constant......Page 141 Law of Reciprocity......Page 145 Principle of Continuity......Page 150 Exercises......Page 163 CHAPTER IX - LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS......Page 164 Solution of Linear Equations of Differences in series......Page 171 Finite Solution of Equations of Differences......Page 174 Binomial Equations......Page 176 Exercises......Page 191 CHAPTER X - OF EQUATIONS OF PARTIAL AND OF MIXED DIFFERENCES, AND OF SIMULTANEOUS EQUATIONS OF DIFFERENCES......Page 192 Equations of Partial Differences......Page 195 Method of Generating Functions......Page 204 Equations of Mixed Differences......Page 206 Simultaneous Equations......Page 218 Exercises......Page 219 CHAPTER XI - OF THE CALCULUS OF FUNCTIONS......Page 221 Direct Problems......Page 222 Periodical Functions......Page 228 Functional Equations......Page 231 Exercises......Page 242 CHAPTER XII - GEOMETRICAL APPLICATIONS......Page 245 Answers to the Exercises......Page 258 Leather Binding on Spine and Corners with Golden Leaf Printing on round Spine (extra customization on request like complete leather, Golden Screen printing in Front, Color Leather, Colored book etc.) Reprinted in 2019 with the help of original edition published long back [1860]. This book is printed in black & white, sewing binding for longer life, Printed on high quality Paper, re-sized as per Current standards, professionally processed without changing its contents. As these are old books, we processed each page manually and make them readable but in some cases some pages which are blur or missing or black spots. If it is multi volume set, then it is only single volume, if you wish to order a specific or all the volumes you may contact us. We expect that you will understand our compulsion in these books. We found this book important for the readers who want to know more about our old treasure so we brought it back to the shelves. Hope you will like it and give your comments and suggestions. - eng, Pages 282. EXTRA 10 DAYS APART FROM THE NORMAL SHIPPING PERIOD WILL BE REQUIRED FOR LEATHER BOUND BOOKS. COMPLETE LEATHER WILL COST YOU EXTRA US$ 25 APART FROM THE LEATHER BOUND BOOKS. {FOLIO EDITION IS ALSO AVAILABLE.} George Boole, the father of Boolean algebra, published A Treatise on the Calculus of Finite Differences in 1860. It was an instant classic, and later became the basis for our contemporary digital computer systems. The book explains finite calculus, explores various problem-solving equations, and provides exercises for students.