文档介绍：THE MATHEMATICS OF NMR
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Exponential Functions
Trigonometric Functions
Differentials and Integrals
Vectors
Matrices
Coordinate Transformations
Convolutions
Imaginary Numbers
The Fourier Transform
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Exponential Functions
The number occurs so often in calculations that it is given the symbol e. When e is raised to the power x, it is often written exp(x).
ex = exp(x) =
Logarithms based on powers of e are called natural logarithms. If
x = ey
then
ln(x) = y,
Many of the dynamic NMR processes are exponential in nature. For example, signals decay exponentially as a function of time. It is therefore essential to understand the nature of exponential curves. mon exponential functions are
y = e-x/t
y = (1 - e-x/t)
y = (1 - 2e-x/t)
where t is a constant.
Trigonometric Functions
The basic trigonometric functions sine
and cosine
describe sinusoidal functions which are 90o out of phase.
The trigonometric identities are used in geometric calculations.
Sin(q) = Opposite / Hypotenuse
Cos(q) = Adjacent / Hypotenuse
Tan(q) = Opposite / Adjacent
The function sin(x) / x occurs often and is called sinc(x).
Differentials and Integrals
A differential can be thought