MATH 157 Lecture Notes - Lecture 5: Parametric Equation

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 157
• Professor: Shiva Gol Tabaghi

Document Summary

13. 1 vector functions and space curves: puzzle. Using six matches of equal length, form four equilateral tri- angles: problem. Describe the motion of the particle whose coordinates at time t are x = cos t and y = 0 and z = sin t: generalization. The changing location of a point moving along the parametric curve can be described by giving its position vector r(t) = x(t)i + y(t)j + z(t)k = hx(t), y(t), z(t)i: example. Describe the motion of the particle whose position vector is r(t) = i cos t + j sin t + tk: vector-valued function. Any function that associates with the number t the vector r(t) is called a vector-valued function. 2 (a) the limit of a vector-valued function r = hf, g, hi is de ned by lim t a t a t a t a r(t) = hlim.