Partial Differential Equations
The Taylor series expansion is a mathematical representation that expresses a function as an infinite sum of terms calculated from the values of its derivatives at a single point. This concept allows us to approximate complex functions using polynomials, which can be particularly useful in stability analysis and linearization when examining the behavior of dynamical systems near equilibrium points. By using Taylor series, we can simplify the analysis of stability and assess how small perturbations affect the system's performance.
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