0195136047.pdf

834 APPENDIX B Self and mutual inductance Section 1.2 Stored energy Section 1.2 AC circuits Average and rms values Section 1.1 ...

APPENDIX C Technical Terms, Units, Constants, and Conversion Factors for the SI System C.1Physical Quantities C.2Prefixes C.3Phy ...

836 APPENDIX C TABLE C.2Prefixes Prefix Symbol Meaning exa E 1018 peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto ...

TECHNICAL TERMS, UNITS, CONSTANTS, AND CONVERSION FACTORS FOR THE SI SYSTEM 837 Continued TABLE C.4Continued energy 1 joule (J) ...

APPENDIX D Mathematical Relations D.1Trigonometric Functions D.2Exponential and Logarithmic Functions D.3Derivatives and Integra ...

MATHEMATICAL RELATIONS 839 4 cos^3 (x)=3 cos(x)+cos( 3 x) 8 sin^4 (x)= 3 −4 cos( 2 x)+cos( 4 x) 8 cos^4 (x)= 3 +4 cos( 2 x)+cos( ...

840 APPENDIX D D.3 DERIVATIVES AND INTEGRALS Derivatives: d dx (a)= 0 ,whereais a fixed real number d dx (x)= 1 d dx (au)=a du d ...

MATHEMATICAL RELATIONS 841 ∫ x^2 dx (a^2 +x^2 )^2 = −x 2 (a^2 +x^2 ) + 1 2 a tan−^1 x a ∫ lnxdx=xlnx−x ∫ eaxdx= eax a ,areal or ...

842 APPENDIX D D.4 SERIES EXPANSIONS AND FINITE SERIES ( 1 ±x)n= 1 ±nx+ n(n− 1 ) 2! x^2 ± n(n− 1 )(n− 2 ) 3! x^3 ±... (x^2 < ...

APPENDIX E Solution of Simultaneous Equations CRAMER’S RULE Cramer’s rule provides an efficient organization for the work that i ...

844 APPENDIX E D 1 = ∣ ∣ ∣ ∣ ∣ ∣ b 1 a 12 a 13 b 2 a 22 a 23 b 3 a 32 a 33 ∣ ∣ ∣ ∣ ∣ ∣ =b 1 ∣ ∣ ∣ ∣ a 22 a 23 a 32 a 33 ∣ ∣ ∣ ∣− ...

SOLUTION OF SIMULTANEOUS EQUATIONS 845 c 22 x 2 +c 23 d 3 c 33 =d 2 or x 2 = 1 c 22 [ −c 23 d 3 c 33 +d 2 ] (8b) Substituting Eq ...

APPENDIX F Complex Numbers j= √ − 1 = 1  90 ◦;j^2 =− 1 = 1  180 ◦;j^3 =−j= 1  270 ◦= 1  − 90 ◦;j^4 = 1  0 ◦ e±jθ=cosθ±jsinθ ...

APPENDIX G Fourier Series A periodic waveformf(t)=f(t+T), which is said to be periodic with a periodT, fundamental frequencyf= 1 ...

848 APPENDIX G c 0 = a 0 2 (8) c ̄n= 1 2 (an−jbn), n= 1 , 2 , ... (9) c ̄−n= 1 2 (an+jbn)= ̄c∗n,n= 1 , 2 , ... (10) where the as ...

FOURIER SERIES 849 f(t)has odd symmetry such thatf(−t)=−f(t), its Fourier series will have no cosine terms; that is to say, alla ...

850 APPENDIX G − π^2 4 sin 4 πt k +( π^2 5 − 4 53 )sin 5 πt k +... ] ( 0 <t<k) (30) t^2 = k^2 3 − 4 k^2 π^2 [ cos πt k − 1 ...

APPENDIX H Laplace Transforms Iff(t)is a piecewise continuous real-valued function of the real variablet( 0 ≤t<∞), and |f(t)| ...

852 APPENDIX H ∫t 0 f(τ)g(t−τ ) dτ F (s)G(s) Multiplication byt (frequency differentiation) tf (t) − d ds[F(s)] Division byt (fr ...

LAPLACE TRANSFORMS 853 sin(ωt+θ) ssinθ+ωcosθ (s^2 +ω^2 ) cosωt s s^2 +ω^2 cos(ωt+θ) scosθ−ωsinθ (s^2 +ω^2 ) e−atsinωt ω (s+a)^2 ...