A software package that supports the construction of Poincare maps is required for the problems in this section.
Compute and graph the points of the Poincare map with
The equation
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Fundamentals of Differential Equations and Boundary Value Problems
- Information on curve in Exercise 37-40, as well as many other curves, is available on the Famous Curve section of the MacTutor History of Mathematics Archive website at www-history.mcs.st-and.ac.uk/-history. The graph of 3(x2+y2)2=25(x2y2), shown in the figure, is an lemniscate of Bernoulli. Find the equation of the tangent line at point (2,1).arrow_forwardShooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.arrow_forwardFind an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_forward
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