Algebra, an Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges: Pt. 1 & 2 (AMS Chelsea Publishing No. 84 7th Revised ed
By: George Chrystal (author)Hardback
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In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions. The range of entries in the Subject Index is very wide. To mention a few out of many hundreds: Horner's method, multinomial theorem, mortality table, arithmetico-geometric series, Pellian equation, Bernoulli numbers, irrationality of $e$, Gudermanian, Euler numbers, continuant, Stirling's theorem, Riemann surface. This volume includes over 2,400 exercises with solutions.
Volume I: Fundamental laws and processes of algebra Monomials--Laws of indices--Degree Theory of quotients--First principles of theory of numbers Distribution of products--Elements of the theory of rational integral functions Transformation of the quotient of two integral functions Greatest common measure and least common multiple Factorisation of integral functions Rational fractions Further applications to the theory of numbers Irrational functions Arithmetical theory of surds Complex numbers Ratio and proportion On conditional equations in general Variation of a function Equations and functions of first degree Equations of the second degree General theory of integral functions Solution of problems by means of equations Arithmetic, geometric, and allied series Logarithms Theory of interest and annuities Appendix Results of exercises Index for parts I and II Volume II: Permutations and combinations General theory of inequalities Limits Convergence of infinite series and of infinite products Binomial and multinomial series for any index Exponential and logarithmic series Summation of the fundamental power-series for complex values of the variable General theorems regarding the expansion of functions in infinite forms Summation and transformation of series in general Simple continued fractions On recurring continued fractions General continued fractions General properties of integral numbers Probability, or the theory of averages Results of exercises Index of proper names for parts I and II Index for parts I and II.
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- ID: 9780821819319
7th Revised edition
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