Higher Engineering Mathematics

702 FOURIER SERIES Imaginary axis 024 Real axis ω = 2 rad/s ω = 2 rad/s Figure 74.10 (b) From equation (3), page 690, cosθ= 1 2 ...

THE COMPLEX OR EXPONENTIAL FORM OF A FOURIER SERIES 703 L Now try the following exercise. Exercise 250 Further problems on phaso ...

Assign-19-H8152.tex 23/6/2006 15: 18 Page 704 Fourier series Assignment 19 This assignment covers the material contained in Chap ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 705 Essential formulae Number and Algebra Laws of indices: am×an=am+n am an =am−n (am)n=a ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 706 706 ESSENTIAL FORMULAE Arithmetic progression: Ifa=first term andd=common difference, ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 707 ESSENTIAL FORMULAE 707 Triangle formulae: With reference to Fig. FA2: Sine rule a sin ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 708 708 ESSENTIAL FORMULAE s θ r r Figure FA3 For sector of circle: s=rθ (θin rad) shaded ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 709 ESSENTIAL FORMULAE 709 Complex equations:Ifm+jn=p+jqthenm=p andn=q Multiplication:z 1 ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 710 710 ESSENTIAL FORMULAE yorf(x) dy dx orf′(x) cosec−^1 f(x) −f′(x) f(x) √ [f(x)]^2 − 1 ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 711 ESSENTIAL FORMULAE 711 Tangents and normals Equation of tangent to curvey=f(x) at the ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 712 712 ESSENTIAL FORMULAE Integral Calculus Standard integrals y ∫ ydx axn a xn+^1 n+ 1 ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 713 ESSENTIAL FORMULAE 713 ∫π 0 xncosxdx=In=−nπn−^1 −n(n−1)In− 2 ∫ xnsinxdx=In=−xncosx+nx ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 714 714 ESSENTIAL FORMULAE Second moment of area and radius of gyration Shape Position of ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 715 ESSENTIAL FORMULAE 715 Perpendicular axis theorem: IfOXandOYlie in the plane of areaA ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 716 716 ESSENTIAL FORMULAE Numerical solutions of first order differential equations Eule ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 717 ESSENTIAL FORMULAE 717 Leibniz’s theorem To find then’th derivative of a producty=uv: ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 718 718 ESSENTIAL FORMULAE J 0 (x)= 1 − x^2 22 (1!)^2 + x^4 24 (2!)^2 − x^6 26 (3!)^2 +·· ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 719 ESSENTIAL FORMULAE 719 Chi-square distribution Percentile values (χ^2 p) for the Chi- ...

Ess-For-H8152.tex 19/7/2006 18: 2 Page 720 720 ESSENTIAL FORMULAE Laplace Transforms Function Laplace transforms f(t) L{f(t)}= ∫ ...

Index-H8152.tex 23/6/2006 15: 18 Page 721 Index Adjoint of matrix, 274 Algebra, 1 Algebraic method of successive approximations, ...