Tom M. Apostol - Calculus, Volume II_ Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability. Vol. 2-John Wiley & Sons (1969)

... that s - I = But s - t E Sand t1 - s1 E SL so s - t is both orthogonal to tl - sL and equal to t1 - & Since the zero element is the only element orthogonal to itself, we must have s - t = This... (yl,yl)= jT1t2dt+, to obtain y2(t) = x2(t) - (E; ye(t) - E$l; yl(t) = t2 - 17 03 Similarly, we find that y3(t) = t3 - St, y4(t) = t4 - $t2 + -& , y5(t) = t5 - -gt3 + &t www.pdfgrip.com 26 Linear spaces... fields, and applications to partial differential equations and extremum problems Integral calculus includes line integrals, multiple integrals, and surface integrals, with applications to vector