This dissertation examines the application of various classical root finding methods to digital maximum power point tracking (DMPPT). An overview of root finding methods such as the Newton Raphson Method (NRM), Secant Method (SM), Bisection Method (BSM), Regula Falsi Method (RFM) and a proposed Modified Regula Falsi Method (MRFM) applied to photovoltaic (PV) applications is presented. These methods are compared among themselves. Some of their features are also compared with other commonly used maximum power point (MPP) tracking methods. Issues found when implementing these root finding methods based on continuous variables in a digital domain are explored. Some of these discussed issues include numerical stability, digital implementation of differential operators, and quantization error. Convergence speed is also explored. The analysis is used to provide practical insights into the design of a DMPPT based on classical root finding algorithms. A new DMPPT based on a MRFM is proposed and used as the basis for the discussion. It is shown that this proposed method is faster than the other discussed methods that ensure convergence to the MPP. The discussion is approached from a practical perspective and also includes theoretical analysis to support the observations. Extensive simulation and experimental results with hardware prototypes verify the analysis. / text