By S. Lipschutz
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Additional resources for Finite Mathematics [Schaum's Outlines]
Sample text
Is given by V = V 1 + V 2 ~- V 3 --}- . . )k Product of a vector V by a scalar quantity s sV = (sa)i + (sb)j + (sc)k (S 1 + s 2 ) V = S l Y + s2V ( V 1 + V2)s = V l S + V2s where sV has the same direction as V, and its magnitude is s times the magnitude of V. Scalar product of two vectors, V1"V2 VI°V2 : IVlllV21cos~ Vector product of two vectors, V 1 X V 2 V 1 X V21=]Vl[lV21sin where ~b is the angle between V1 and V2. Derivatives of vectors d dB dA dt(A'B)=A'-~-+B' d~-- de If e(t) is a unit vector ~ - is perpendicular to e: de that is e • ~ -- 0.
10 M a t r i c e s A matrix which has an array of m × n numbers a r r a n g e d in m r o w s a n d n c o l u m n s is c a l l e d a n m × n m a t r i x . It is d e n o t e d by: all a12 ... aln a21 a22 ... a2n aml am2 ... a rnn 36 Aeronautical Engineer's Data Book Square matrix This is a matrix having the same number of rows and columns. al, a12 a13] I a00] a21 a22 a23/ is a square matrix of order 3 × aBi a32 a33] 3. Diagonal matrix This is a square matrix in which all the elements are zero except those in the leading diagonal.
X7 7! 6 7 + ... (x a < 1) 30 Aeronautical Engineer's Data Book tan-lx=x-lx3+5xS-- ~i X7 + ... 7 Vector algebra Vectors have direction and magnitude and satisfy the triangle rule for addition. Quantities such as velocity, force, and straight-line displacements may be represented by vectors. g. Ax, Ay, A z or Axi + A j + Azk. , is given by V = V 1 + V 2 ~- V 3 --}- . . )k Product of a vector V by a scalar quantity s sV = (sa)i + (sb)j + (sc)k (S 1 + s 2 ) V = S l Y + s2V ( V 1 + V2)s = V l S + V2s where sV has the same direction as V, and its magnitude is s times the magnitude of V.