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Adams P.W., Smith K., Výborný D. — Introduction to Mathematics with Maple
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Название: Introduction to Mathematics with MapleАвторы: Adams P.W., Smith K., Výborný D.Аннотация: Adams (University of Queensland, Australia) introduces university level mathematics, covering both algebra and calculus, in this text for first- and second-year students. Because it treats the material in depth, the book can also be of interest to beginning graduate students. The text aims for a balanced treatment, presenting material which requires deep understanding and also encouraging readers to use Maple software for computations and experiments. Coverage progresses from sets, functions, and real numbers through derivatives, elementary functions, and integrals. Chapter exercises are included, along with an appendix on Maple programming.
Язык: Рубрика: Руководства по программному обеспечению /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 523Добавлена в каталог: 13.12.2009Операции: Положить на полку |
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! 11 " 8 # 13 43 43 43 43 43 43 xi % 8 * 11 + 11 - 11 / 11 1 72 := 18 ; 6 ? 9 Abel 220 306 467 abs 76 Algebra 18 Antiderivative 455 arccot 427 Archimedes 309 498 arcsin 425 arctan 426 Argand 199 arithmetical operators 11 Arrow, Kenneth 54 Assigning variables 18 Axiom of Choice 236 Axiom, least upper bound 114 116 Axioms 1 53 Axioms, Euclid 55 Axioms, field 97 Axioms, GF( 2 99 192 Axioms, GF(4) 193 Axioms, order 100 Axioms, Peano 121 Axioms, ring 57 98 BACKSPACE 7 Barrow.I 498 bernoulli 309 Bernoulli, inequality 157 Bernoulli, J 390 Bernoulli, rule 390 392 Binomial coefficient 400 Bolzano 271 273 Bolzano — Cauchy principle 451 Bolzano, function 402 Bound, lower 115 Bound, upper 115 Bounded 115 Bounded, bounded above 115 Bounded, bounded below 115 Cantor, Georg, diagonal process 235 Cardano H. 221 Cartesian product (see Sets Cartesian case sensitivity 7 Cauchy 270 309 Cauchy, condensation test 304 Cauchy, convergence principle 272 Cauchy, definition 324 Cauchy, mean value theorem 388 Cauchy, product 308 Cavalieri 498 Ceil 76 Change of variables 472 476 Characteristic function 72 Coefficient binomial 400 Cohen, Paul 56 Comments 13 Complex number, absolute value 196 Complex number, complex conjugate 196 Complex number, geometric representation 199 Complex number, imaginary 196 Complex number, imaginary part 195 Complex number, purely imaginary 196 Complex number, real part 195 Complex number, square root 197 Complex number, trigonometric form 199 Constants in Maple 12 Continuity at a point 332 Continuity from the left 333 Continuity from the right 333 Continuity of the inverse 340 Continuity on intervals 338 Continuity, uniform 346 Convergence, uniform 493 cos 76 cosh 430 cot 427 Cousin, lemma 343 Darboux, property 355 de Morgan, Augustus 44 Decinmal fraction 162 Dedekind 124 306 Dedekind cut 124 Definition, Cauchy 324 Definition, derivative 358 Definition, limit 316 Definition, limit from the left 313 Definition, limit from the right 313 Definitions, 153 Definitions, Absolute and Conditional Convergence 293 Degree of a polynomial 171 Denjoy.A 500 Derivative from the left 359 Derivative from the right 359 Derivative, definition 358 Descartes R. 218 Dini 401 Dini, derivate 401 Dini, derivates 401 Dirichlet 306 Divisor 184 Domain 63 D’Alembert 498 D’Alembert, limit test 298 D’Alembert, test 297 e 12 Euclid 51 55 Euler 488 Euler, formulae 421 Euler’s integral 488 492 Evalf() 16 Exact numbers 13 14 EXP 76 Expression sequence 39 Fermat 498 Ferro del S. 221 Field, isomorphic 171 Floating point number 14 Floating point numbers 13 FLOOR 76 Formal power series 169 Formula, reduction 471 Formula, Wallis 470 Formulae, Euler 421 Formulae, Fourier J. 218 Fraction, decimal 162 Function 69 Function, bijection 90 Function, decreasing 257 Function, increasing 257 Function, injective 90 Function, inverse 91 Function, one-to-one 90 Function, onto 90 Function, periodic 419 Function, step 450 Function, surjective 90 Function, uniformly continuous 346 Functions in Maple 75 Galois 220 Gamma 492 gamma, function 492 Gauss K. F. 213 Gauss K. F., greatest lower bound 117 Gauss, plane 199 Godel, Kurt 55 56 Hake 484 490 Hake’s theorem 484 490 498 499 Heaviside, help 9 Heaviside, Oliver 72 Henstock, R 431 Hermite, C. 261 Hilbert, David 237 HORNER 180 If statement 502 Increasing at a point 378 Induction hypothesis 131 Inequality, arithmetic-geometric mean 158 Inequality, Bernoulli 157 Inference 131 Infimum 117 Inflection 385 integral 438 472 Integral domain 174 Integral, definition 438 Integral, over unbounded intervals 489 Integration by parts 468 Integration by substitution 472 476 Interrupting commands 7 interval 104 Interval, closed 104 Interval, end points 104 Interval, open 104 Isomorphic 171 Isomorphism 171 Kepler 498 Kronecker, Leopold 113 Kurzweil, integrable 438 Lagrange 480 Lagrange, mean value theorem 387 480 Lagrange, remainder 480 481 Laplace 495 Laplace, integral 495 Lebesgue, axioms 499 Lebesgue, Henri 498 Lebesgue, integration 499 Leibniz 498 Leibniz, formula 380 Leibniz, series 414 Leibniz, test 292 Library of functions 75 Limit at infinity 316 Limit inferior 353 Limit superior 353 LIST 39 ln 76 local 504 LOG 76 Maclaurin 400 Maple, commands 513 Maple, integration 443 Maple, Using, collect () 24 Maple, Using, convert() 17 Maple, Using, diff() 360 Maple, Using, Digits() 15 Maple, Using, expand() 21 Maple, Using, factor() 22 Maple, Using, int() 443 Maple, Using, normal() 23 Maple, Using, simplify() 22 Maple, Using, sort() 24 MAX 76 Maximum, local 375 Mean, arithmetic 158 Mean, geometric 157 MIN 76 Minimum, local 375 Moivre 201 multiple commands 7 Newton 498 Newton, binomial theorem 150 Newton, Leibniz formula 457 nops 502 Oresme 309 Peano 477 Peano, axiomatic approach 166 Peano, axioms 121 127 Peano, Giuseppe 114 Peano, remainder 397 Perron. 0 500 PI 12 Polya, G 134 Polynomial 167 170 Polynomial, unending 169 Polynomials, multiplication 170 173 Polynomials, ring of 170 Previous results 8 proc 501 Products in Maple 143 Quitting Maple 8 Raabe, inverse 91 Raabe, radius of convergence 301 Raabe, range 63 Raabe, reducible 185 Raabe, reflexive 66 Raabe, relation 63 Raabe, symmetric 66 Raabe, test 304 Raabe, transitive 66 Riemann, Bernard 306 Riemann, integrable 438 Riemann, ring isomorphic 171 Riemann, ring of polynomials 170 Riemann, sum 432 Root, multiple 217 Root, primitive of unity 204 Root, rational 214 Ruffini Paulo 220 Russell, Bertrand 53 Scheme, Homer 180 semicolons 6 SEQUENCE 145 Sequence, decreasing 257 Sequence, Fibonacci 148 Sequence, increasing 257 Series, formal power 169 Set, countable 232 Sets, cartesian product 43 Sets, countable 232 Sets, difference 36 Sets, Enumerable 232 Sets, intersection 35 Sets, union 35 sgn 74 Signum 74 sin 76 Singleton 53 sinh 430 spaces 7 sqrt 11 76 Starting Maple 4 Statement if 502 Step function 450 Stopping Maple 8
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