Solving the Quintic: Dominant Balance Analysis

This lecture delves into the dominant balance analysis of solving the quintic polynomial, exploring the non-dimensionalization process and the identification of distinct limits. By using rigorous expansion methods and series expansions, the coefficients in the expansion are calculated order-by-order. The lecture demonstrates the process of balancing terms and evaluating the accuracy of approximate solutions. The analysis reveals the behavior of roots as the parameter varies, highlighting the importance of symbolic expressions in understanding the solution's behavior. The lecture concludes with insights into the significance of dominant balance analysis in obtaining a deeper understanding of complex problems.