Unformatted text preview: THE TRASECTORY "FOLLOWS" THE CHANGE ARROWS : * Pirand - Lindeled Theorum : V. imp. - The Curere is everyonere tangent to the vector field One Print, One Trojetores" ss the function does not change too fast Clicken Qi can trajectories cuess? I No, because the change reelers dont cross & trajectory eloesn't ende A) Yes, belause traveetonies arole around vertical line test -> No, because trajectories Do B) No, because of the satisfy the vorticel love test olen every point in time, we " have a single thique plur c) No, because veetan fields are functions > CORRECT NOTE: in a 3D model, there is only APPRENT self-crossing. In reality, they overlap but don't touch. EULER'S METHODby X'=0.2*** (2-(, step sice 001 , find next state + x 1 x 1 x'-st 1 x+QX .At) 0 401 4.8 | 0.048 40+ 0.048 +40.048 ON 40.08EULER'S METHOD IN 2D our oppreximation to the red cusure ure a w Green acerou > change vector Blue Wrows= change vector. At - X+(X' 07) your approximation to the red cutive value at that point NOTE to increase accurace and reduce theor LOWER st.