Higher Engineering Mathematics, Sixth Edition
662 Higher Engineering Mathematics The circle: With reference to Fig. FA3. Area=πr^2 Circumference= 2 πr πradians= 180 ◦ r s r ...
Essential formulae 663 Complex Numbers z=a+jb=r(cosθ+jsinθ)=r∠θ=rejθ where j^2 =− 1 Modulusr=|z|= √ (a^2 +b^2 ) Argumentθ=argz=t ...
664 Higher Engineering Mathematics yorf(x) dy dx orf′(x) cos−^1 f(x) −f′(x) √ 1 −[f(x)]^2 tan−^1 x a a a^2 +x^2 tan−^1 f(x) f′(x ...
Essential formulae 665 Maximum and minimum values: Ify=f(x)then dy dx = 0 for stationary points. Let a solution of dy dx =0bex=a ...
666 Higher Engineering Mathematics Integral Calculus Standard integrals: y ∫ ydx axn a xn+^1 n+ 1 +c (except wheren=−1) cosax 1 ...
Essential formulae 667 ∫π 0 xncosxdx=In=−nπn−^1 −n(n− 1 )In− 2 ∫ xnsinxdx=In=−xncosx+nxn−^1 sinx −n(n− 1 )In− 2 ∫ sinnxdx=In=− 1 ...
668 Higher Engineering Mathematics Second moment of area and radius of gyration: Shape Position of axis Second moment Radius of ...
Essential formulae 669 Simpson’s rule ∫ ydx≈ 1 3 ( width of interval )[( first+last ordinate ) + 4 ( sum of even ordinates ) + 2 ...
670 Higher Engineering Mathematics (iii) if the roots of the auxiliary equation are: (a) real and different,saym=αandm=β then th ...
Essential formulae 671 (ii) differentiate the trial series to find y′ andy′′, (iii) substitutethe results in thegiven differenti ...
672 Higher Engineering Mathematics Themodeis the most commonly occurring value in a set of data. Standard deviation: σ= √√ √ √ [ ...
Essential formulae 673 on a small sample size 74.5 Estimating the mean of a population based (σknown): The confidence coefficien ...
674 Higher Engineering Mathematics The Laplace transforms of derivatives: First derivative L { dy dx } =sL{y}−y(0) wherey( 0 )is ...
Index Adding alternating waveforms, 265 Adjoint of matrix, 239 Algebra, 1–12 Algebraic method of successive approximations, 81–8 ...
676 Index Differential coefficient, 288 Differential equations, 445 a d^2 y dx^2 +b dy dx +cy=0 type, 477–482 a d^2 y dx^2 +b dy ...
Index 677 Imaginary part, 213 Implicit differentiation, 320–324 Implicit function, 320 Independent event, 548 Indices, laws of, ...
678 Index integration, using, 409–413 linear factors, 13–15, 409–411 quadratic factors, 16–17, 412–413 repeated linear factors, ...
Index 679 parallel axis, 384–385 perpendicular axis, 385 Pythagoras, 97–98 Total differential, 351–352 Transfer function, 598 Tr ...
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