Morse Theory
A Taylor series expansion is a mathematical representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. This concept is essential for approximating functions and understanding their behavior near that point, making it a powerful tool in various areas of mathematics, including critical point analysis. By using Taylor series, one can determine how functions behave near critical points by analyzing the coefficients of the series, which relate to the function's derivatives.
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