THE MATHEMATICS OF NMR Exponential Functions Differentials and Integrals Matrices Coordinate Transformations Convolutions The Fourier transform Exponential Functions The number 2.71828183 occurs so often in calculations that it is given the symbol e. When e is aised to the power x, it is often written exp(x) e=exp(x)=2.71828183 Logarithms based on powers of e are called natural logarithms. If 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. Three common exponential functions are y=e-X/t y=(1-e-x/t)THE MATHEMATICS OF NMR -------------------------------------------------------------------------------- Exponential Functions Trigonometric Functions Differentials and Integrals Vectors Matrices Coordinate Transformations Convolutions Imaginary Numbers The Fourier Transform -------------------------------------------------------------------------------- Exponential Functions The number 2.71828183 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). e x = exp(x) = 2.71828183x 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. Three common exponential functions are y = e-x/t y = (1 - e-x/t)