I think it would be much more valuable to learn how the algorithms inside the graphing calculator work, instead of learning how to use a calculator. Integration

I think it would be much more valuable to learn how the algorithms inside the graphing calculator work, instead of learning how to use a calculator. Integration, differential equation solving and root finding can be programmed in just a couple lines of code. It is amazing how well these numerical methods work. E.g. solving the differential equation y' = y from t=0,y=1 to t=1 computes exp(1): import math def simple(f,t,t1,y=0.0,dt=0.001): while t<t1: y += f(t,y)*dt t += dt return y def rk4(f,t,t1,y=0.0,dt=0.001): while t<t1: k1 = f(t,y) k2 = f(t+dt/2, y+dt*k1/2) k3 = f(t+dt/2, y+dt*k2/2) k4 = f(t+dt, y+dt*k3) y += (k1+2*k2+2*k3+k4)*dt/6 t += dt return y def f(t,y): return y print "Simple:", simple(f, 0.0, 1.0, 1.0) print " RK4:", rk4(f, 0.0, 1.0, 1.0) print "math.e:", math.e This prints: Simple: 2.71692393224 RK4: 2.71828182846 math.e: 2.71828182846 Or perhaps Newton's method to solve x^2 = 2, solution x=sqrt(2): def newton(f, fprime, x=0.1, n=10): for i in xrange(0,n): x -= f(x)/fprime(x) return x def g(x): return x**2 - 2 def gprime(x): return 2*x # derivative of g print newton(g, gprime) print math.sqrt(2) Result: 1.41421356237 1.41421356237 Note that 10 iterations are enough to get all the digits that Python prints correct. In just 13 lines of code we have tools for effectively solving any ordinary differential y' = f(t,y) equation and for solving f(x) = 0 for many functions f. Solving y' = f(t,y) where f(t,y) is a function of t alone gives us integration. E.g. integrating 1/t from t=1 to t=2: rk4(lambda t,y: 1/t, 1.0, 2.0) (but there are better methods for integration than general purpose differential equation solvers)