Concept

Taylor series

Related lectures (29)

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Taylor Development: Higher Derivatives

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Power Series: Convergence and Applications

Covers the theory of power series, focusing on convergence criteria and applications.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Approximation of Functions by Taylor Polynomials

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

Functions Extension and Taylor Expansion

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Generalized Integral: Comparison Criteria and Taylor Series

Explores series convergence criteria, generalized integrals, and Taylor series applications.

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Power series and Taylor series

Covers power series, Taylor series, and their applications in functions like logarithmic functions.

Differential Calculation: Hyperbolic Functions

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Power series and Taylor series

Covers the properties of improper integrals, power series, and Taylor series.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

Cauchy Sequences and Series

Explores Cauchy sequences, convergence, bottoms, and series with illustrative examples.

Convergence Criteria

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