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Maclaurin Series
Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specified function. Let us start out with a few notation and definitions that we'll require.
To find out a condition that must be true in order for a Taylor series to exist for a function let's first describe the nth degree Taylor polynomial of f (x) as,
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Note: This actually is a polynomial of degree at most n! If we were to write out the sum with no the summation notation this would obviously be an nth degree polynomial.
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Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these
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Simpson's Rule - Approximating Definite Integrals This is the last method we're going to take a look at and in this case we will once again divide up the interval [a, b] int
x2+y2 r=12
For a first order linear differential equation the solution process is as given below: 1. Place the differential equation in the correct initial form, (1). 2. Determine the i
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