Handbook of mathematics for engineers and scienteists p83art doc
Handbook of mathematics for engineers and scienteists part 1 ppsx
... 8 1. 3. PowersandLogarithms 8 1. 3 .1. PowersandRoots 8 1. 3.2. Logarithms 9 1. 4. BinomialTheoremandRelatedFormulas 10 1. 4 .1. Factorials. Binomial Coefficients.BinomialTheorem 10 1. 4.2. RelatedFormulas ... 1 10 /16 /06 2:53: 21 PMCONTENTSAuthors xxvPreface xxviiMain Notation xxix Part I. Definitions, Formulas, Methods, and Theorems 1 1. Arithmetic and Elementary Algebra 3 1. 1. RealNumbers 3 1. 1 .1. ... RelatedFormulas 10 1. 5. Arithmetic and Geometric Progressions. Finite Sums and Products . . . . . . . . . . . . . . . . . 11 1. 5 .1. ArithmeticandGeometricProgressions 11 1. 5.2. Finite Series and Products...
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Handbook of mathematics for engineers and scienteists part 2 doc
... GeneralFormofIntegralTransforms.SomeFormulas 43511.1.1. IntegralTransformsandInversionFormulas 43511.1 .2. Residues.JordanLemma 43511 .2. LaplaceTransform 43611 .2. 1. LaplaceTransformandtheInverseLaplaceTransform ... LinearSystemsofOrdinaryDifferentialEquations 528 12. 6.1. Systems of Linear Constant-CoefficientEquations 528 12. 6 .2. Systems of Linear Variable-CoefficientEquations 539 12. 7. NonlinearSystemsofOrdinaryDifferentialEquations 5 42 12. 7.1. ... Coefficients 514 12. 4 .2. Linear Equations with Variable Coefficients 518 12. 4.3. AsymptoticSolutionsofLinearEquations 522 12. 4.4. CollocationMethodandItsConvergence 523 12. 5. NonlinearEquationsofArbitraryOrder...
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Handbook of mathematics for engineers and scienteists part 3 ppsx
... 930 ReferencesforChapter17 935 18. Special Functions and Their Properties 937 18.1. Some Coefficients,Symbols,andNumbers 937 18.1.1. Binomial Coefficients 937 18.1.2. PochhammerSymbol 938 18.1 .3. ... Equation and a Nonlinear Wave Equation 733 15.10. DifferentialConstraintsMethod 737 15.10.1. DescriptionoftheMethod 737 15.10.2. First-OrderDifferentialConstraints 739 15.10 .3. Second- and Higher-Order ... Condition for Systems of LinearEquations 75715.12 .3. Solution of the Cauchy Problem by the Inverse Scattering Problem Method 76015. 13. ConservationLawsandIntegralsofMotion 76615. 13. 1. Basic...
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Handbook of mathematics for engineers and scienteists part 4 potx
... Press, 1995 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, ... 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 Nonlinear Partial DifferentialEquation, ... the Department of Applied Mathematics at Bauman Moscow State Technical University, professor of mathematics at MoscowState University of Engineering and Computer Science, vice-chairman of Mathematics and...
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Handbook of mathematics for engineers and scienteists part 5 potx
... stands for the union of sets A and B∩ intersection (Boolean multiplication); A ∩B stands for the intersection (com-mon part) of sets A and B⊂ inclusion; A ⊂ B means that the set A is part of ... of numbers a and b is denoted by a + b and has the propertya + b = b + a– minus sign; the difference of numbers a and b is denoted by a – b⋅ multiplication sign; the product of numbersa and ... Alexei Zhurov for fruitful discussions and valuable remarks. We also appreciate the help of Vladimir Nazaikinskii and GrigoriiYosifian for translating several chapters of this book and are thankful...
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Handbook of mathematics for engineers and scienteists part 6 ppsx
... integerp 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 integer ... m/n,wherem and n are natural numbers:ap= am/n=n√am, a ≥ 0. 6 ARITHMETIC AND ELEMENTARY ALGEBRA1.2.2. Addition and Multiplication of Numbers1.2.2-1. Addition of real numbers.The sum of real ... A and |b| ≤ B it follows that |a + b| ≤ A + B and |ab| ≤ AB.1.3. Powers and Logarithms1.3.1. Powers and Roots1.3.1-1. Powers and roots: the main definitions.Given a positive real number a and...
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Handbook of mathematics for engineers and scienteists part 7 docx
... right-handsides of the above formulas is called the index of summation (for series) or the index of multiplication (for products). The 1 and n (or the m and n)aretheupper and lower limits of summation ... b2).1.6. MEAN VALUES AND INEQUALITIES OF GENERAL FORM 131.6. Mean Values and Inequalities of General Form1.6.1. Arithmetic Mean, Geometric Mean, and Other Mean Values.Inequalities for Mean Values1.6.1-1. ... 3b)+nab. A large number of formulas for the summation of various finite series can be found inSection T1.1.10 ARITHMETIC AND ELEMENTARY ALGEBRA1.4. Binomial Theorem and Related Formulas1.4.1. Factorials....
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Handbook of mathematics for engineers and scienteists part 8 pps
... (Napierian) logarithms, and the function ex:e = limn→∞1 +1nn= 2.7 182 81 , ex= limn→∞1 +xnn.The formula for passing from an arbitrary base a to the base e of natural logarithms:ax= ... modulus of the logarithmic function tends to infinity slower than anypower of x as x → +∞; and it tends to zero slower than any power of 1/x as x → +0.Thegraphs of the functions y =log2x and y ... = limn→∞1 +1nn= 2.7 182 81 Formulas for passing from an arbitrary base a to the Napierian base e:logax =ln xln a.Differentiation and integration formulas:(ln x)=1x,ln...
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Handbook of mathematics for engineers and scienteists part 9 pot
... 2πn]. For x =π2+ 2πn, it attains its maximal value (y = 1), and for x =–π2+ 2πn it attains its minimal value (y =–1). The graph of the function y =sinx iscalled the sinusoid or sine curve and ... The graph of the function y =cotx isgiveninFig.2 .9. O1xyππ1yx= tanπ2π2Figure 2.8. The graph of the function y =tanx.O1xyππ1yx= cotπ2π23π2Figure 2 .9. The graph of the function ... on everysegment [–π + 2πn, 2πn] and is a decreasing function on every segment [2πn, π + 2πn],n = 0,1, 2, For x = 2πn it attains its maximal value (y = 1), and for x = π + 2πnit attains its...
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Handbook of mathematics for engineers and scienteists part 10 pdf
... each of the semiaxes of its domain;it has no points of extremum and does not cross the coordinate axes. It has two horizontalasymptotes: y =–1 (as x → –∞)andy = 1 (as x → +∞). The graph of the ... its domain with no points of extremum. The graph of the function y =sinhx is given in Fig. 2.14.2.4.1-3. Hyperbolic cosine: y =coshx.This function is defined for all x, and its range is y [1,+∞). ... graph of the function y =sinhx.O112234xy12yxcosh=Figure 2.15. The graph of the function y =coshx.2.4.1-4. Hyperbolic tangent: y =tanhx.This function is defi ned for all x, and its...
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Handbook of mathematics for engineers and scienteists part 11 ppsx
... 1).References for Chapter 2Abramowitz,M.andStegun,I.A.(Editors) ,Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics, ... 1998.Korn,G.A.andKorn,T.M.,Mathematical Handbook for Scientists and Engineers, 2nd Edition, DoverPublications, New York, 2000.Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, ... properties and relations characterizing plane trianglesNo.The name of property Properties and relations1Triangle inequalityThe length of any side of a triangle does not exceedthe sum of lengths of...
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Handbook of mathematics for engineers and scienteists part 13 doc
... area of the triangle with vertices at 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 ... 3.21b). 13. For secants, AC ⋅ AD = AB ⋅ AE = m2– R2(Fig. 3.21c).14. For a tangent and a secant, AF ⋅ AF = AC ⋅ AD (Fig. 3.21c).3.1.3-2. Segment and sector.Aplanefigure bounded by two radii and ... legs are of equallength. The line segment connecting the midpoints of the legs is called the median of thetrapezoid. The length of the median is equal to half the sum of the lengths of the bases,m...
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Handbook of mathematics for engineers and scienteists part 14 ppt
... = 2R and d = 2r are the outer and inner diameters, ρ =12(R + r) is the midradius, and δ = R – r is the width of the annulus.The area of the part of the annulus contained in a sector of central ... on one side of each of its faces. The sum∠AOB +∠BOC + ···+∠EOA of face angles (Fig. 3.25a) of any convex polyhedral angleis less that 2π (or 360◦).4◦.Asolid angle is a part of space bounded ... volume of the frustum isV =13h(S1+ S2+S1S2)=13hS21 +aA+a2A2,(3.2.2.7)where S1 and S2are the areas of the bases, a and A are two respective sides of the bases,and...
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Handbook of mathematics for engineers and scienteists part 15 pot
... 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◦.Thesphere of radius R centered at O is the set of points in space ... h),(3.2.3.10)where 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 conicalsurface whose base is the base of the ... called a spherical zone, and the plane circular surfaces are the bases of a spherical segment. The radius R of theball, the radii a and b of the bases, and the height h of a spherical segment...
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Handbook of mathematics for engineers and scienteists p83art doc
... undecidedcbODomain of instabilityDomain of instabilityDomain of stabilityStability undecidedIIVIIIIIFigure 12.10. Domains of stability and instability of the trivial solution of system (12.7.3.11).2. ... autonomous system of the form (12.7.2.5) can be reduced to an(n – 1)-dimensional system of equations independent of x. To this end, one should selectone of the equations and divide the other ... integrals (12.7.2.3) and (12.7.2.4) are independent. Hence, using them, one can express y2 and y3in terms of y1 and then substitute the resulting expressions into the first equation of system (12.7.2.2)....
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