LEADER 00862nam0-2200313---450- 001 990008748790403321 005 20081106133204.0 010 $a0-8493-0068-1 035 $a000874879 035 $aFED01000874879 035 $a(Aleph)000874879FED01 035 $a000874879 100 $a20081106d2003----km-y0itay50------ba 101 0 $aeng 105 $ay-------001yy 200 1 $aEarthquake engineering handbook$fWai-Fah Chen$gCharles Scawthorn 205 $a1 210 $aLondon$cCRC Press$d2003 215 $aXXIII, p.$cill.$d23 cm 610 0 $aGeotecnica 700 1$aChen,$bWai Fah$043045 701 1$aScawthorn,$bCharles$0503980 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990008748790403321 952 $a15 GT-L4-36$b152$fDINID 959 $aDINID 996 $aEarthquake engineering handbook$9719757 997 $aUNINA LEADER 05152nam 2200493 450 001 996466389803316 005 20231110223927.0 010 $a3-030-75051-5 035 $a(CKB)4940000000613691 035 $a(MiAaPQ)EBC6734187 035 $a(Au-PeEL)EBL6734187 035 $a(OCoLC)1269094774 035 $a(PPN)258052368 035 $a(EXLCZ)994940000000613691 100 $a20220624d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElements of mathematics $ea problem-centered approach to history and foundations /$fGabor Toth 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (534 pages) 225 1 $aUndergraduate Texts in Mathematics 300 $aIncludes index. 311 $a3-030-75050-7 327 $aIntro -- Preface -- Why This Book? -- Audience -- The Historical Context -- In Closing: Gelfand's Teaching Legacy -- Acknowledgment -- Contents -- 0 Preliminaries: Sets, Relations, Maps -- 0.1 Sets -- Exercises -- 0.2 Relations -- Exercise -- 0.3 Maps and Real Functions -- Exercises -- 0.4 Cardinality -- Exercises -- 0.5 The Zermelo-Fraenkel Axiomatic Set Theory* -- Exercise -- 1 Natural, Integral, and Rational Numbers -- 1.1 Natural Numbers -- Exercises -- 1.2 Integers -- Exercises -- 1.3 The Division Algorithm for Integers -- Exercises -- 1.4 Rational Numbers -- Exercises -- 2 Real Numbers -- 2.1 Real Numbers via Dedekind Cuts -- Exercises -- 2.2 Infinite Decimals as Real Numbers -- Exercises -- 2.3 Real Numbers via Cauchy Sequences -- Exercises -- 2.4 Dirichlet Approximation and Equidistribution* -- Exercises -- 3 Rational and Real Exponentiation -- 3.1 Arithmetic Properties of the Limit -- Exercises -- 3.2 Roots, Rational and Real Exponents -- Exercises -- 3.3 Logarithms -- Exercises -- 3.4 The Stolz-Cesàro Theorems -- Exercises -- 4 Limits of Real Functions -- 4.1 Limit Inferior and Limit Superior -- Exercise -- 4.2 Continuity -- Exercise -- 4.3 Differentiability -- Exercises -- 5 Real Analytic Plane Geometry -- 5.1 The Birkhoff Metric Geometry -- Exercise -- 5.2 The Cartesian Model of the Birkhoff Plane -- Exercises -- 5.3 The Cartesian Distance -- Exercise -- 5.4 The Triangle Inequality -- Exercise -- 5.5 Lines and Circles -- Exercises -- 5.6 Arc Length on the Unit Circle -- Exercise -- 5.7 The Birkhoff Angle Measure -- Exercises -- 5.8 The Principle of Shortest Distance* -- Exercises -- 5.9 ? According to Archimedes* -- Exercise -- 6 Polynomial Expressions -- 6.1 Polynomials -- Exercises -- 6.2 Arithmetic Operations on Polynomials -- Exercises -- 6.3 The Binomial Formula -- Exercises -- 6.4 Factoring Polynomials -- Exercises. 327 $a6.5 The Division Algorithm for Polynomials -- Exercises -- 6.6 Symmetric Polynomials -- Exercises -- 6.7 The Cauchy-Schwarz Inequality -- Exercises -- 7 Polynomial Functions -- 7.1 Polynomials as Functions -- Exercises -- 7.2 Roots of Cubic Polynomials -- Exercises -- 7.3 Roots of Quartic and Quintic Polynomials -- Exercise -- 7.4 Polynomials with Rational Coefficients -- Exercises -- 7.5 Factoring Multivariate Polynomials -- Exercises -- 7.6 The Greatest Common Factor -- Exercise -- 8 Conics -- 8.1 The General Conic -- Exercise -- 8.2 Parabolas -- Exercises -- 8.3 Ellipses -- Exercises -- 8.4 Hyperbolas -- Exercises -- 9 Rational and Algebraic Expressions and Functions -- 9.1 Rational Expressions and Rational Functions -- Exercises -- 9.2 The Partial Fraction Decomposition -- Exercises -- 9.3 Asymptotes of Rational Functions -- Exercises -- 9.4 Algebraic Expressions and Functions, Rationalization -- Exercises -- 9.5 Harmonic, Geometric, Arithmetic, Quadratic Means -- Exercises -- 9.6 The Greatest Integer Function -- Exercises -- 10 Exponential and Logarithmic Functions -- 10.1 The Natural Exponential Function According to Newton -- Exercises -- 10.2 The Bernoulli Numbers* -- Exercise -- 10.3 The Natural Logarithm -- Exercises -- 10.4 The General Exponential and Logarithmic Functions -- Exercise -- 10.5 The Natural Exponential Function According to Euler -- Exercises -- 11 Trigonometry -- 11.1 The Unit Circle S vs. the Real Line R -- Exercise -- 11.2 The Sine and Cosine Functions -- Exercises -- 11.3 Principal Identities for Sine and Cosine -- Exercises -- 11.4 Trigonometric Rational Functions -- Exercises -- 11.5 Trigonometric Limits -- Exercises -- 11.6 Cosine and Sine Series According to Newton -- Exercise -- 11.7 The Basel Problem of Euler* -- Exercise -- 11.8 Ptolemy's Theorem -- Exercise -- Further Reading -- Index. 410 0$aUndergraduate Texts in Mathematics 606 $aMathematics$xHistory 606 $aHistòria de la matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics$xHistory. 615 7$aHistòria de la matemàtica 676 $a510 700 $aTo?th$b Ga?bor$f1964-$01243451 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466389803316 996 $aElements of mathematics$92884162 997 $aUNISA