pull examples and complete homework 1

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diff --git a/examples/FallingBall3.jl b/examples/FallingBall3.jl
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+#!/Applications/Julia-1.8.app/Contents/Resources/julia/bin/julia
+
+using Plots # for plotting trajectory
+using DifferentialEquations # for solving ODEs
+
+g = 9.8 # acceleration of gravity in m/s^2
+
+t_final = 1.0 # final time of trajectory
+p = 0.0 # parameters (not used here)
+
+function tendency!(dyv::Vector{Float64}, yv::Vector{Float64}, p, t::Float64) # ! notation tells us that arguments will be modified
+   y = yv[1] # 2D phase space; use vcat(x, v) to combine 2 vectors
+   v = yv[2] # dy/dt = v
+   a = -g # dv/dt = -g
+
+   dyv[1] = v 
+   dyv[2] = a
+end
+
+y0 = 10.0 # initial position in meters
+v0 = 0.0 # initial velocity in m/s
+yv0 = [y0, v0] # initial condition in phase space 
+tspan = (0.0, t_final) # span of time to simulate
+
+prob = ODEProblem(tendency!, yv0, tspan, p) # specify ODE
+sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8) # solve using Tsit5 algorithm to specified accuracy
+
+println("\n\t Results")
+println("final time  = ", sol.t[end])
+println("y = ", sol[1, end], " and v = ", sol[2, end])
+println("exact v = ", v0 - g * t_final)
+println("exact y = ", y0 + v0 * t_final - 0.5 * g * t_final^2.0)
+
+plot(sol, idxs = (1)) # plot position as a function of time