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Cloud M.J., Drachman B.C. — Inequalities: with applications to engineering
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Название: Inequalities: with applications to engineeringАвторы: Cloud M.J., Drachman B.C. Аннотация: There used to be a saying in mathematical circles that went something like "Children work with equalities; grownups work with inequalities. " An overstatement perhaps, but a facility with inequalities does seem to be necessary for an understanding of much of mathematics at intermediate and higher levels. In particular, a working knowledge of inequalities can be beneficial to the practicing engineer. Inequalities are central to the definitions of all limiting processes, including differention and integration. When exact solutions are unavailable, inconvenient, or unnecessary, inqualities can be used to obtain error bounds for numerical approximation. Inqualities can also lead to an understanding of the qualitative behavior of solutions. This guide to inequalities was written specifically with engineers and other applied scientists in mind. It is intended to help fill the gap between college-algebra level treatments of inqualities that everyone has seen before, and the formidable treatise on the subject that exist in the mathematics literature. Every chapter ends with a rich collection of exercises. The book should be accessible to senior-level engineering students, graduate students, and practicing engineers.
Язык: Рубрика: Математика /Анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 150Добавлена в каталог: 14.04.2005Операции: Положить на полку |
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Предметный указатель
Absolute value 5 Air resistance 82 Algebra of inequalities 2 AM-GM inequality 38 49—51 Arithmetic mean 15 39 50 Arithmetic-geometric mean 124 Asymptotic sequence 70 Axioms of order 2 Bernoulli's inequality 37 Bessel's inequality 65 Bound, Chernoff 111 Bound, greatest lower 4 Bound, least upper 4 Bounded, above, below 4 Bounded, function 19 Capacitance 90 Cauchy mean value theorem 25 Cauchy sequence 54 59 Cauchy — Schwarz inequality 44 60 61 66 Chebyshev's inequality 45 51 110 Communication 112 Complementary exponents 41 complete 55 Continuity 20 62 Contraction mapping 56 Contraction mapping, theorem 56 Control 109 Convergence 6 54 Convergence in mean 123 Convergence, pointwise 69 Convergence, uniform 69 123 Convolution 68 Dense 36 DMS 114 Duality 121 Eigenvalues 93 Elliptic integral 125 entropy 114 Equation, Laplace 89 Equation, Poisson 88 Estimation of integrals 29 67 Euler method 75 Euler's constant 36 Euler's formula 84 extrema 21 Fibonacci numbers 15 Fixed point 56 Fourier coefficients 65 Fourier series 65 69 85 Fourier transform 101 Fredholm integral equation 116 Function, autocorrelation 124 Function, Bessel 78 82 124 Function, bounded 19 Function, coerror 125 Function, complementary error 124 Function, continuity 20 Function, convex 46 Function, convolution 68 Function, decreasing 21 Function, elliptic integral 125 Function, exponential integral 77 123 Function, Gamma 77 123 Function, increasing 21 Function, Lyapunov 104 Function, monotonic 21 35 Function, square integrable 51 Function, terminology and facts 19 Function, transfer 108 Geometric mean 15 39 50 geometric shapes 84 Gibb's phenomenon 100 Give a little 11 Green's formula 90 Harmonic mean 15 40 50 Harmonic-geometric-arithmetic means inequality 50 Heron's formula 87 Hilbert space 62 Hoelder's inequality 40 42 43 50 Implicit function theorem 119 Inequality of the means 38 49—51 Inequality, AM-GM 38 49—51 Inequality, Bernoulli 37 Inequality, Bessel 65 Inequality, Cauchy — Schwarz 44 60 61 66 Inequality, Chebyshev 45 51 110 Inequality, convexity 46 Inequality, harmonic-geometric-arithmetic means 50 Inequality, harmonic-geometric-arithmetic means for integrals 50 Inequality, Hoelder 40 42 43 50 Inequality, integral 21 Inequality, isoperimetric 85 Inequality, Jensen 46 51 52 Inequality, Jordan 29 Inequality, Kantorovich 50 Inequality, logarithmic 27 Inequality, Markov 110 Inequality, Minkowski 43 61 66 Inequality, modulus 22 Inequality, Ostrowski 35 Inequality, quadratic 5 Inequality, Schur 97 Inequality, triangle 7 58 Inequality, Weierstrass 14 Inequality, Young 38 41 49 Infimum 4 information 113 114 Inner product 59 62 Inner product space 59 Intermediate value property 21 Isoperimetric inequality 85 Iterative process 56 Jensen's inequality 46 51 52 Jordan's inequality 29 Kantorovich's inequality 50 l'Hopital's monotone rule 25 Lagrange interpolation 72 Laplace equation 89 Laplace transform 108 Law, parallelogram 61 Law, transitive 3 LIMIT 6 Limit point 54 Linear space 57 Lipschitz condition 33 117 Logarithmic inequality 27 Lyapunov function 104 Mapping 55 Mapping, continuous 55 Mapping, contraction 56 Markov's inequality 110 Matched filter 112 Matrix 93 Matrix, conjugate transpose 93 Matrix, eigenvalues 93 Matrix, hermitian 93 Matrix, norm 98 Matrix, symmetric 94 Matrix, trace 96 Maximum 4 Mean value theorem 24 Mean Value Theorem for Integrals 23 35 Mean value theorem, Cauchy 25 Mean, arithmetic 15 39 50 Mean, arithmetic-geometric 124 Mean, geometric 15 39 50 Mean, harmonic 15 40 50 Metric 54 Metric space 53 Minimizing vector 62 Minimum 4 Minkowski's inequality 43 61 66 Modulus inequality 22 Monotonicity, conditions for 25 Motor control 109 Neighborhood 6 54 Neumann series 117 Newton's method 120 125 Noise 112 Norm 58 62 Norm, 58 Norm, 97 Norm, compatible 99 Norm, cubic 98 Norm, Frobenius 98 Norm, induced 61 Norm, matrix 97 Norm, supremum 58 Order, exponential 34 Order, symbols O,o 19 Orthogonal projection 62 Orthogonality 62 Orthonormal set 62 Ostrowski's inequality 35 Parallelogram law 61 Parseval's identity 85 Persistence of sign 20 55 Picard iteration 56 125 Picard — Lindeloef theorem 117 Platonic solids 85 Poisson's equation 88 Polyhedron 84 Polynomial 82 Polynomial, Chebyshev 78 Polynomial, Legendre 79 Polynomial, orthogonal 81 Polynomial, orthogonal, zeros of 81 Positive definite 95 104 Principle, Dirichlet 91 Principle, maximum 89 Principle, squeeze 14 20 Principle, uncertainty 102 Projectile problem 82 Pythagorean Theorem 62 Quadratic form 94 Quadratic inequality 5 Results from differential calculus 23 Riemann integral 21 Riemann lemma 65 Riemann sum 21 Rolle's theorem 25 Schur's inequality 97 Second Derivative Test 26 95 SEQUENCE 6 Sequence, asymptotic 70 Sequence, increasing 10 Sequence, monotonic 17 Set, closed 54 Set, open 54 Simpson's rule 72 123 Space, 65 Space, function 58 Space, Hilbert 62 Space, inner product 59 Space, linear 57 Space, metric 53 Space, metric, complete 55 Space, normed linear 58 Spectral radius 99 Spring, nonlinear 105 Square integrable 51 68 Squeeze principle 14 20 Stability 103 107 Stability, asymptotic 103 Stability, BIBO 107 Stability, exponential 103 Stability, Lyapunov 103 Steiner symmetrization 92 Successive approximations 56 Supremum 4 Sylvester's criterion 94 Taylor's method 74 123 Taylor's theorem 24 Telescoping property 15 Theorem, contraction mapping 56 Theorem, fundamental, of calculus 23 Theorem, implicit function 119 Theorem, l'Hopital's monotone 25 Theorem, mean value 24 Theorem, mean value for integrals 23 35 Theorem, mean value, Cauchy 25 Theorem, Picard — Lindeloef 117 Theorem, Pythagorean 62 Theorem, Rolle 25 Theorem, Taylor 24 Transfer function 108 Transform, Fourier 101 Transform, Laplace 108 Triangle inequality 7 58 Wallis's product 34 Weierstrass's inequality 14 Young's inequality 38 41 49 Zeros of polynomials, bounds 9
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