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Steinmetz Decoded

Engineering Mathematics Foundations

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Why This Family Matters

Section titled “Why This Family Matters”

Routes the mathematical language Steinmetz used to train engineers in calculation itself.

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candidate records in this family.

273

reviewable relation candidates.

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sources represented.

Candidate Formula Cards

Section titled “Candidate Formula Cards”
#1Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3090
(Let A = a(\cos a+j \sin a) be divided by J5 = 6(\cos ,5+y \sin /5),)
OCR source lineLet A = a(cos a+j sin a) be divided by J5 = 6(cos ,5+y sin /5),
#2Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3131
(If, A=ai +ja2 = a (\cos a+j \sin a), then)
OCR source lineIf, A=ai +ja2 = a (cos a+j sin a), then
#3Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2398
(and ai + ja2 = a (\cos 6 + j \sin d) ;)
OCR source lineand ai + ja2 = a (cos 6 + j sin d) ;
#4Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2400
(or ai —ja2 = A(\cos 0+j \sin 6).)
OCR source lineor ai -\-ja2 = A(cos 0+j sin 6).
#5Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2414
(and A ==5 (\cos 37 ^\circ H-j \sin 37 ^\circ).)
OCR source lineand A ==5 (cos 37 deg. H-j sin 37 deg).
#6Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2844
(C = AB = ah (\cos a+j \sin a) (\cos /?+ / \sin /5))
OCR source lineC = AB = ah (cos a+j sin a) (cos /?+ / sin /5)
#7Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3115
(A = ai +ja2 = a(\cos a+j \sin a),)
OCR source lineA = ai +ja2 = a(cos a+j sin a),
#8Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2282
(20. If ai+y6i=6+2.5 J is represented by the point \pi;)
OCR source line20. If ai+y6i=6+2.5 J is represented by the point Pi;
#9Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2284
(and the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-)
OCR source lineand the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-
#10Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1783
(\pi: a:=+3, y= +2 P2: x= +S y= -2,)
OCR source linePi: a:=+3, y= +2 P2: x= +S y= -2,
#11Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1788
(• \pi=3+2/ P2 = 3-2/ P3=-3+2/ P4=-3-2y)
OCR source line• Pi=3+2/ P2 = 3-2/ P3=-3+2/ P4=-3-2y
#12Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1830
(\pi = - -^a, P2 = - 7— a,)
OCR source linePi = - -^a, P2 = - 7— a,
#13Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1861
(V +l=\cos qX + 7 sm qX - ,)
OCR source lineV +l=cos qX + 7 sm qX - ,
#14Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1982
(\cos x+y \sin X = ~1,)
OCR source linecos x+y sin X = ~1,
#15Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2041
(a+y6 = 3 4-2?s, the point P2, 90 ^\circ away from \pi, would)
OCR source linea+y6 = 3 4-2?s, the point P2, 90 deg. away from Pi, would
#16Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2044
(P2 = jPi-Ka+jb)=j(3-V2j)= -2+3/,)
OCR source lineP2 = jPi-Ka+jb)=j(3-V2j)= -2+3/,
#17Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2291
(izontal distances of \pi and P2: ao = ai+a2 = 6+3 = 9, and a)
OCR source lineizontal distances of Pi and P2: ao = ai+a2 = 6+3 = 9, and a
#18Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2296
(ao +jho = {ai +a2) +j(bi +62))
OCR source lineao +jho = {ai +a2) +j(bi +62)
#19Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2339
(a2 +jb2 = (ao -di) +j(bo -61))
OCR source linea2 +jb2 = (ao -di) +j(bo -61)
#20Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2380
(^ = a(\cos 0 +j \sin d),)
OCR source line^ = a(cos 0 +j sin d),
#21Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2489
(but since ai=a \cos 6 is negative, -4, \cos 6 must be negative,)
OCR source linebut since ai=a cos 6 is negative, -4, cos 6 must be negative,
#22Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2492
(4 = 5 (\cos 217 ^\circ +j \sin 217 ^\circ))
OCR source line4 = 5 (cos 217 deg. +j sin 217 deg.)
#23Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2493
(= 5( - \cos 37 ^\circ -j \sin 37 ^\circ))
OCR source line= 5( - cos 37 deg. -j sin 37 deg.)
#24Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2584
(^0 = So (\cos do +j \sin ^0))
OCR source line^0 = So (cos do +j sin ^0)
#25Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2610
(isi,n 6i=j^ = 0A50, as ^i = 24.3deg.)
OCR source lineisi,n 6i=j^ = 0A50, as ^i = 24.3deg.
#26Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2638
(♦^2 = S2(\cos d2 +j \sin dz))
OCR source line♦^2 = S2(cos d2 +j sin dz)
#27Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2689
(/S4 = 1105 (\cos 30 ^\circ +y \sin 30 ^\circ))
OCR source line/S4 = 1105 (cos 30 deg. +y sin 30 deg.)
#28Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2727
(S6 = sq{\cos Oq +/ \sin Oq))
OCR source lineS6 = sq{cos Oq +/ sin Oq)
#29Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2772
(AB = {aihi -a2?>2) +j{aih2 +^2*^1),)
OCR source lineAB = {aihi -a2?>2) +j{aih2 +^2*^1),
#30Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2785
(For instance, A=2+j multiplied by B=^l+1.5 j gives)
OCR source lineFor instance, A=2+j multiplied by B=^l+1.5 j gives
#31Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2846
(= a6 {\cos (a +/?) +j \sin (a +/5)} :)
OCR source line= a6 {cos (a +/?) +j sin (a +/5)} :
#32Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2855
(Thus, to multiply the vector quantity, A = ai+ja2 = a (\cos)
OCR source lineThus, to multiply the vector quantity, A = ai+ja2 = a (cos
#33Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2856
(« + y \sin^ by ^ = 61 +J62 = & (\cos /? +f \sin ^) the vector OA in Fig.)
OCR source line« + y sin^ by ^ = 61 +J62 = & (cos /? +f sin ^) the vector OA in Fig.
#34Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3122
(A = 3 +4/ = 5(\cos 53 ^\circ +/ \sin 53 ^\circ);)
OCR source lineA = 3 +4/ = 5(cos 53 deg. +/ sin 53 deg.);
#35Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3125
((7 = 44 = 54(\cos 4 X53 ^\circ +j \sin 4 X53 ^\circ) ■)
OCR source line(7 = 44 = 54(cos 4 X53 deg. +j sin 4 X53 deg.) ■
#36Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3126
(= 625(\cos 212 ^\circ +j \sin 212 ^\circ))
OCR source line= 625(cos 212 deg. +j sin 212 deg.)
#37Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3135
((7 = A/A = A”=a”(\cos-+7sin-))
OCR source line(7 = A/A = A”=a”(cos-+7sin-)
#38Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3147
(A = a(ios{a—2q7:)—j ^m.{a+2qn),)
OCR source lineA = a\(ios{a-\-2q7:)-\-j ^m.{a+2qn)\,
#39Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3177
(C= ■<lA= i625(\cos ^ - —+jsm 1 ^))
OCR source lineC= ■<lA= i625(cos ^ - —+jsm 1 ^)
#40Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3179
(= 5(\cos 53 + j \sin 53) = 3 + ij)
OCR source line= 5(cos 53 + j sin 53) = 3 + ij
#41Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3181
(= 5(\cos 143 +j \sin 143) =5( -\cos 37 +f \sin 37) = -4+3/)
OCR source line= 5(cos 143 +j sin 143) =5( -cos 37 +f sin 37) = -4+3/
#42Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3182
(= 5(\cos 233 + J \sin 233) = 5( -\cos 53 + / \sin 53) = -3 + 4/)
OCR source line= 5(cos 233 + J sin 233) = 5( -cos 53 + / sin 53) = -3 + 4/
#43Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3183
(= 5(\cos 323 +y \sin 323) =5(\cos 37 -j \sin 37) =4-3/)
OCR source line= 5(cos 323 +y sin 323) =5(cos 37 -j sin 37) =4-3/
#44Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1609
(in opposite direction from A, Inversely, if we take AC= -2,)
OCR source linein opposite direction from A, Inversely, if we take AC= -2,
#45Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1739
(vertical distance, jBP= +2f, and therefore is given by a)
OCR source linevertical distance, jBP= +2f, and therefore is given by a
#46Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1972
(If jx = \og, (-1), then £^’^= -1,)
OCR source lineIf jx = \og, (-1), then £^’^= -1,
#47Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2293
(\pi and P2: 6o = &amp;i+&amp;2 = 2.5+4 = 6.5, hence, is given by the)
OCR source linePi and P2: 6o = &i+&2 = 2.5+4 = 6.5, hence, is given by the
#48Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2581
(per sec, making an angle ^o = 20 ^\circ with the x-axis; hence,)
OCR source lineper sec, making an angle ^o = 20 deg. with the x-axis; hence,
#49Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2764
(24. If A = ai+ja2 and B = hi—jb2, are two general, or)
OCR source line24. If A = ai+ja2 and B = hi-\-jb2, are two general, or
#50Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2973
(If now we have two impedances, OZi and OZ2, Zi =ri -jxi)
OCR source lineIf now we have two impedances, OZi and OZ2, Zi =ri -jxi
#51Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2980
(If we have a current and a voltage, I = ii + ji2 and E = ei —je2,)
OCR source lineIf we have a current and a voltage, I = ii + ji2 and E = ei -\-je2,
#52Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3173
(For instance, let 4= -529-33iy = 625 (\cos 212 ^\circ+)
OCR source lineFor instance, let 4= -529-33iy = 625 (cos 212 deg.+
#53Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2474
(but since ai = a \cos 6 is negative, ~4, \cos 6 must be negative,)
OCR source linebut since ai = a cos 6 is negative, ~4, cos 6 must be negative,
#54Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2801
(a2 = a \sin a)
OCR source linea2 = a sin a
#55Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1600
(tance AB, and multiply by (-1)^ we get the distance AC= -2)
OCR source linetance AB, and multiply by (-1)^ we get the distance AC= -2
#56Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1610
(and multiply by (-1), we get AB=+2; that is, multiplica-)
OCR source lineand multiply by (-1), we get AB=+2; that is, multiplica-
#57Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1614
(more by V-l, we’ get +2 X v^^X V~l= -2; that is,)
OCR source linemore by V-l, we’ get +2 X v^^X V~l= -2; that is,
#58Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1740
(combination of the distances, 05= +3 and BP=- +2/. For)
OCR source linecombination of the distances, 05= +3 and BP=- +2/. For
#59Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1785
(Ps’ x=-S, y=+2 P4: x=-S y=-2])
OCR source linePs’ x=-S, y=+2 P4: x=-S y=-2]
#60Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1820
(x= - = and 2/ = - =/; or, is represented by the general nuniber,)
OCR source linex= - = and 2/ = - =/; or, is represented by the general nuniber,
#61Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 1991
(\log£(-l)=/7r(2n + l),)
OCR source linelog£(-l)=/7r(2n + l),
#62Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2068
(jhk= +1.)
OCR source linejhk= +1.
#63Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2117
(khj= -1,)
OCR source linekhj= -1,
#64Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2148
(The only feature which must be kept in mind is that f = - 1, and)
OCR source lineThe only feature which must be kept in mind is that f = - 1, and
#65Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2159
(f =/, f= -1, f = -], f- +1;)
OCR source linef =/, f= -1, f = -], f- +1;
#66Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2160
(f = +y, f= -1, f= -/,, f = +i;)
OCR source linef = +y, f= -1, f= -/,, f = +i;
#67Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2187
(x+jy = 5-Sj,)
OCR source linex+jy = 5-Sj,
#68Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2190
(x = 5 and y= -3.)
OCR source linex = 5 and y= -3.
#69Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2195
(the general number a+jh = 6+2.5j may be considered as)
OCR source linethe general number a+jh = 6+2.5j may be considered as
#70Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2197
(distance from the y axis, 0A = BP = a^6, and the vertical)
OCR source linedistance from the y axis, 0A = BP = a^6, and the vertical
#71Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2211
(\tan <? = :== =-77- fl/)^‘)
OCR source linetan <? = :== =-77- fl/)^‘
#72Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2242
(\tan 6=-.)
OCR source linetan 6=-.