list of exercises exercise explore rounding errors with large numbers exercise write test functions for xdx exercise rectangle methods exercise adaptive integration exercise integrating raised to exercise integrate products of sine functions exercise revisit fit of sines to function exercise derive the trapezoidal rule for double integral exercise compute the area of triangle by monte carlo integration exercise geometric construction of the forward euler method exercise make test functions for the forward euler method exercise implement and evaluate heun' method exercise find an appropriate time steplogistic model exercise find an appropriate time stepsir model exercise model an adaptive vaccination campaign exercise make sirv model with time-limited effect of vaccination exercise refactor flat program exercise simulate oscillations by general ode solver exercise compute the energy in oscillations exercise use backward euler scheme for population growth exercise use crank-nicolson scheme for population growth exercise understand finite differences via taylor series exercise use backward euler scheme for oscillations exercise use heun' method for the sir model exercise use odespy to solve simple ode exercise set up backward euler scheme for oscillations exercise set up forward euler scheme for nonlinear and damped oscillations exercise discretize an initial condition exercise simulate diffusion equation by hand exercise compute temperature variations in the ground exercise compare implicit methods exercise explore adaptive and implicit methods exercise investigate the rule exercise compute the diffusion of gaussian peak exercise vectorize function for computing the area of polygon exercise explore symmetry exercise compute solutions as exercise solve two-point boundary value problem exercise understand why newton' method can fail exercise see if the secant method fails exercise understand why the bisection method cannot fail exercise combine the bisection method with newton' method exercise write test function for newton' method exercise solve nonlinear equation for vibrating beam