Polynomial Approximation of Differential Equations

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Focusing on spectral methods, this book explores approximate solution techniques for differential equations using classical orthogonal polynomials. It highlights their growing popularity as a competitive alternative to traditional methods, particularly in analyzing periodic solutions through trigonometric and algebraic polynomials. Aimed at beginners, it provides foundational mathematical concepts, essential formulas, and theorems, all presented in an accessible manner without requiring prior knowledge of functional analysis. The book encourages practical experimentation and skill enhancement in numerical applications.