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Dive into a comprehensive 26-minute video lecture on Taylor's Theorem presented by University of Oxford mathematician Dr. Tom Crawford. Derive Taylor's Theorem for approximating functions as polynomials and understand its practical applications through two detailed examples. Begin with an introduction to function approximation using polynomials, then explore the conditions for deriving coefficients. Learn how Cauchy's Mean Value Theorem is applied to achieve equality. Work through two fully solved examples: deriving the power series expansion for cosine around zero, and calculating a third-degree polynomial approximation for ln(1+sin(x)) for small x. Access a free worksheet to test your understanding, and utilize the Maple Calculator App for verification. Explore related topics in the Oxford Calculus series, including partial differentiation, critical points, and differential equations. Enhance your calculus knowledge with this in-depth exploration of Taylor's Theorem and its applications.
