{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mws_gen_dif_txt_continuous

# mws_gen_dif_txt_continuous - Chapter 02.02 Differentiation...

This preview shows pages 1–5. Sign up to view the full content.

02.01.1 Chapter 02.02 Differentiation of Continuous Functions After reading this chapter, you should be able to: 1. derive formulas for approximating the first derivative of a function, 2. derive formulas for approximating derivatives from Taylor series, 3. derive finite difference approximations for higher order derivatives, and 4. use the developed formulas in examples to find derivatives of a function. The derivative of a function at x is defined as ( ) ( ) ( ) x x f x x f x f x + = 0 lim To be able to find a derivative numerically, one could make x finite to give, ( ) ( ) ( ) x x f x x f x f + . Knowing the value of x at which you want to find the derivative of ( ) x f , we choose a value of x to find the value of ( ) x f . To estimate the value of ( ) x f , three such approximations are suggested as follows. Forward Difference Approximation of the First Derivative From differential calculus, we know ( ) ( ) ( ) x x f x x f x f x + = 0 lim For a finite x , ( ) ( ) ( ) x x f x x f x f + The above is the forward divided difference approximation of the first derivative. It is called forward because you are taking a point ahead of x . To find the value of ( ) x f at i x x = , we may choose another point x ahead as 1 + = i x x . This gives ( ) ( ) ( ) x x f x f x f i i i + 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document