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Cloud M.J., Drachman B.C. — Inequalities: with applications to engineering
Cloud M.J., Drachman B.C. — Inequalities: with applications to engineering

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Название: Inequalities: with applications to engineering

Авторы: 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: en

Рубрика: Математика/Анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 150

Добавлена в каталог: 14.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $L_{2}$      58
Norm, $L_{p}$      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, $L^{p}$      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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