DRAM 116 Lecture 10: The European Renaissance

5. -stf(t) dt Use the definition of the Laplace transform: le? sin t(s). (12 pts) S/(f)(s) J e t. := 0

Find an equation for the ellipse x2 / 4 + y2 / 16 = 1 in parametric form (x(t) y(t)). (2 sin t, 4 cost), 0 le t le pi (2sin t, 4cost), 0 le t le 2pi (2sin2t, 4cos3t), 0 le t le 2pi / 3 (2 cos2t, 4 sint), 0 le t le 2 pi (2sin 2t, 4cost), 0 le t le pi

2. The error function is widely used in probability theory, theory of errors, and various branches of mathematical physics. The error function is defined by the integral edx Evaluate the following nonlinear integral transforms after changing the order of integration 120] le-pt erf(t)dt I e-pt erf(1/T)dt. and