Taylor Series: Convergence and Applications

Related lectures (29)

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Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Covers the convergence of series and various tests to determine convergence based on odd and even terms.

Explores Newton's method convergence and quadratic convergence properties in theorem 8.4.

Covers absolute convergence, the Leibniz criterion, and series convergence conditions with practical examples.

Covers convergence criteria for series, including comparison, Cauchy's root test, and d'Alembert's ratio test.

Covers the parabolic heat equation in two dimensions and its numerical solution methods.

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Covers numerical methods in physics, focusing on solving complex problems and understanding limitations.

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Explores convergence criteria for series and functions, including the squeeze theorem and D'Alembert's criterion.