Finite Differences

Finite differences are essential for approximating derivatives and solving numerical problems in calculus, particularly in interpolation and differential equations. This chapter outlines three fundamental types: forward, backward, and central differences, each with its respective operators and formulas. Forward differences estimate function changes moving forward, while backward differences track changes in reverse. Central differences, measured around a midpoint, enhance numerical accuracy. Key difference operators, including the shift operator E and averaging operator μ, are introduced with their interrelations.