COMPUTER EXPLORATIONSTrigonometric PolynomialsAs the

Chapter 3, Problem 109E

(choose chapter or problem)

Problem 109E

COMPUTER EXPLORATIONS

Trigonometric Polynomials

As the accompanying figure shows, the trigonometric “polynomial”  gives a good approximation of the sawtooth function s = g(t) on the interval [–π, π]. How well does the derivative of ƒ approximate the derivative of g at the points where dg/dt is defined? To find out, carry out the following steps.

a. Graph dg/dt (where defined) over[–π, π].

b. Find df/dt.

c. Graph df/dt . Where does the approximation of dg/dt by df/dt seem to be best? Least good? Approximations by trigonometric polynomials are important in the theories of heat and oscillation, but we must not expect too much of

them, as we see in the next exercise.