Bronshtein: Handbook of mathematics (2007)

... HANDBOOK OF MATHEMATICS FOR ENGINEERS AND SCIENTISTS C5025_C000a.indd 10 /16 /06 2:53: 21 PM C5025_C000a.indd 10 /16 /06 2:53: 21 PM HANDBOOK OF MATHEMATICS FOR ENGINEERS AND SCIENTISTS Andrei ... Sums and Products 1. 5 .1 Arithmetic and Geometric Progressions 1. 5.2 Finite Series and Products 11 11 12 ... 1. 6.2 Inequalities of General Form 13...

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... 7 .2. 11 Cauchy-Type Singular Integrals 27 3 27 3 27 4 27 6 27 9 28 1 28 3 28 6 28 6 28 7 28 9 29 0 29 5 29 9 301 304 307 308 310 CONTENTS ix 7 .2. 12 Stieltjes ... Convergence of Functions 23 5 23 5 23 7 24 0 24 2 24 3 24 5 24 6 24 9 6 .2 Differential Calculus for Functions of a Single Variable 6 .2. 1 Derivative ... 25 0 25 0 25 2 25 4 25 5 25 7 25...

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... 1 031 20.1.1 Probabilities of Random Events 1 031 20.1.2 Conditional Probability and Simplest Formulas 1 035 20.1 .3 Sequences of Trials ... Method of Quadratures 810 810 811 8 13 815 818 822 8 23 16 .3 Linear Integral Equations of the First Kind with Constant Limits of Integration 16 .3. 1 ... 1175 T3.2.9 Expressions with Special Functions 1176 xx CONTENTS T3 .3 Table...

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... and 2003; A D Polyanin and A V Manzhirov, Handbook of Integral Equations, CRC Press, 1998; A D Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman ... Polyanin, V F Zaitsev, and A Moussiaux, Handbook of First Order Partial Differential Equations, Taylor & Francis, 2002; and A D Polyanin and V F Zaitsev, Handbook of...

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... multiplication); A ∩ B stands for the intersection (common part) of sets A and B inclusion; A ⊂ B means that the set A is part of the set B nonstrict inclusion; A ⊆ B means that the set A is part of the set ... the sum of numbers a and b is denoted by a + b and has the property a+b= b+a minus sign; the difference of numbers a and b is denoted by a – b multiplication s...

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... with integer p and q (q ≠ 0) It is only the rational numbers that can be written in the form of finite (terminating) or periodic (recurring) decimals (e.g., 1/8 = 0.125 and 1 /6 = 0. 166 66 ) Any ... b and c < 0, then ac ≥ bc If < a ≤ b (or a ≤ b < 0), then 1/a ≥ 1/b 6 ARITHMETIC AND ELEMENTARY ALGEBRA 1.2.2 Addition and Multiplication of Numbers 1.2.2-1 Addition of real nu...

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... right-hand sides of the above formulas is called the index of summation (for series) or the index of multiplication (for products) The and n (or the m and n) are the upper and lower limits of summation ... number of formulas for the summation of various finite series can be found in Section T1.1 13 1.6 MEAN VALUES AND INEQUALITIES OF GENERAL FORM 1.6 Mean Values and...

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... 18 ARITHMETIC AND ELEMENTARY ALGEBRA References for Chapter Bronshtein, I N and Semendyayev, K A., Handbook of Mathematics, 4th Edition, Springer-Verlag, Berlin, 2004 Courant, R and Robbins, ... Robbins, H., What Is Mathematics? : An Elementary Approach to Ideas and Methods, 2nd Edition, Oxford University Press, Oxford, 1996 Franklin, J and Daoud, A., Introduction to Proofs...

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... For x = π + 2πn, it attains its maximal value (y = 1), and for 2 x = – π + 2πn it attains its minimal value (y = –1) The graph of the function y = sin x is called the sinusoid or sine curve and ... For x = 2πn it attains its maximal value (y = 1), and for x = π + 2πn it attains its minimal value (y = –1) The graph of the function y = cos x is a sinusoid obtained by shifting...

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... each of the semiaxes of its domain; it has no points of extremum and does not cross the coordinate axes It has two horizontal asymptotes: y = –1 (as x → –∞) and y = (as x → +∞) The graph of the ... axis with no points of extremum It has two horizontal asymptotes y = (as x → +∞) and y = π (as x → –∞) For all x, the following relation holds: arccot x = π – arctan x The graph...

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... References for Chapter Abramowitz, M and Stegun, I A (Editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics, ... Korn, G A and Korn, T M., Mathematical Handbook for Scientists and Engineers, 2nd Edition, Dover Publications, New York, 2000 Prudnikov, A P., Brychkov, Yu A., and Mariche...

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... the center of the disk and at the endpoints of the radii bounding the corresponding sector One takes the minus sign for α < 180 and the plus sign for α > 180 The arc length and the area of a segment ... 3.21b) For secants, AC ⋅ AD = AB ⋅ AE = m2 – R2 (Fig 3.21c) For a tangent and a secant, AF ⋅ AF = AC ⋅ AD (Fig 3.21c) 3.1.3-2 Segment and sector A plane figure bounded b...

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... given by the formula V = SH, where S is the area of the base and H is the altitude of the pyramid (3.2.2.3) The apex of a pyramid is projected onto the circumcenter of the base if one of the following ... S is the area of the base face, H is the altitude of the prism, Psec is the perimeter of a perpendicular section, and Ssec is the area of the perpendicular section, the...

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... R and h are the radius and the height of the spherical cap 3◦ A portion of a ball bounded by the curved surface of a spherical cap and the conical surface whose base is the base of the cap and ... where r is the radius of the upper base and h is the altitude of the frustum of a cone 3.2.3-3 Sphere Spherical parts Torus 1◦ The sphere of radius R centered at O is the s...

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