Advanced mathematics for engineers

Handbook of mathematics for engineers and scienteists part 1 ppsx

... 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 13 14 1. 7 Some Mathematical Methods 1. 7 .1 Proof by Contradiction...

Handbook of mathematics for engineers and scienteists part 2 doc

... 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 9 26 0 6.3 Functions of Several Variables Partial Derivatives 6.3.1 Point Sets Functions Limits and Continuity ...

Handbook of mathematics for engineers and scienteists part 3 ppsx

... 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 Tables of Fourier Cosine Transforms 1177 T3 .3. 1 General...

Handbook of mathematics for engineers and scienteists part 4 potx

... 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 Nonlinear Partial Differential ... compendium of mathematical deﬁnitions, formulas, and theorems intended for researchers, university teachers, engineers, and students of various backgrounds in mathematics The absence of proofs and a...

Handbook of mathematics for engineers and scienteists part 5 potx

... 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 sign; the product of numbers a and b ... convergent ODE and PDE are conventional abbreviations for ordinary differential equation and partial differential equation, respectively Part I Deﬁnitions, Formulas, Methods, and Theorems ...

Handbook of mathematics for engineers and scienteists part 6 ppsx

... 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 numbers The sum of ... > a If a ≤ b and b ≤ a, then a = b If a ≤ b and b ≤ c, then a ≤ c If a < b and b ≤ c (or a ≤ b and b < c), then a < c If a < b and c < d (or c = d), then a + c < b + d If a ≤ b and c > 0, then...

Handbook of mathematics for engineers and scienteists part 7 docx

... 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 Inequalities of General Form 1.6.1 ... assumption of the validity of formula (1 .7. 2.1) for any n it follows that (1 .7. 2.1) is also valid for n + According to the principle of mathematical induction, this proves formula (1 .7. 2.1) ...

Handbook of mathematics for engineers and scienteists part 8 pps

... 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 in Mathematics, Prentice ... Hall, New York, 1 988 Garnier, R and Taylor, J., 100% Mathematical Proof , John Wiley & Sons, New York, 1996 Gelbaum, B R and Olmsted, J M H., Theorems and Counterexamples in Mathematics, Springer-Verlag,...

Handbook of mathematics for engineers and scienteists part 9 pot

... 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 the graph of ... The graph of the function y = cot x is given in Fig 2 .9 y y y = tan x π π y = cot x x O π π Figure 2.8 The graph of the function y = tan x π π O x π π 3π Figure 2 .9 The graph of the function...

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 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 of the function y ... 2.3.2-4 Addition and subtraction of inverse trigonometric functions arcsin x + arcsin y = arcsin x arccos x √ – y + y – x2 arccos y = arccos xy (1 – x2 )(1 – y ) for x2 + y ≤ 1, for x y ≥ 0, 34...

Handbook of mathematics for engineers and scienteists part 11 ppsx

... 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 Marichev, O I., Integrals and Series, ... No The name of property Properties and relations Triangle inequality The length of any side of a triangle does not exceed the sum of lengths of the other two sides Sum of angles of a triangle...

Handbook of mathematics for engineers and scienteists part 13 doc

... 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 by two radii and one of the ... A diameter (b) and a tangent (c) of a circle Properties of circles and disks: √ The circumference is L = 2πR = πd = πS The area of a disk is S = πR2 = πd2 = Ld 4 The diameter of a circle is a...

Handbook of mathematics for engineers and scienteists part 14 ppt

... 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, then the area of the lateral ... 3.26b) The volume of a truncated prism is V = LP1 , (3.2.2.2) where L is the length of the segment connecting the centers of the base faces and P1 is the area of the section of the prism by a...

Xem thêm