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Numerical Dierentiation
5.1
Basic Concepts
This chapter deals with numerical approximations of derivatives. The rst questions
that comes up to mind is: why do we need to approximate derivatives at all? After
all, we do know how to analytically d

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6.1
Numerical Integration
Basic Concepts
In this chapter we are going to explore various ways for approximating the integral of a
function over a given domain. There are various reasons as of why such approximations
can be useful. First, not eve

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2.1
Methods for Solving Nonlinear Problems
Preliminary Discussion
In this chapter we will learn methods for approximating solutions of nonlinear algebraic
equations. We will limit our attention to the case of nding roots of a single equation
of

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Approximations
4.1
Background
In this chapter we are interested in approximation problems. Generally speaking, starting from a function f (x) we would like to nd a dierent function g(x) that belongs
to a given class of functions and is close to

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3.1
Interpolation
What is Interpolation?
Imagine that there is an unknown function f (x) for which someone supplies you with
its (exact) values at (n + 1) distinct points x0 < x1 < < xn , i.e., f (x0 ), . . . , f (xn ) are
given. The interpolati