Lectures related to Nonlinear Equations: Convergence and Taylor Polynomials

Taylor Series: Approximating Functions with Polynomials

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

Calculus Foundations: Taylor Series and Integrals

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Taylor Series: Convergence and Applications

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

Solving Equations: Newton's Method

Covers Newton's method conditions and convergence, extension to multiple variables, and linear models.

Convergence of Series: Solutions and Tests

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

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Taylor Polynomials: Approximating Functions

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

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Approximation of Functions by Taylor Polynomials

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

Resolution Sequence: Defining a Procedure

Explains the systematic procedure for solving flow sheets and stream calculations.

Taylor Polynomials: Correction Exam 2018

Covers the correction of an exam from 2018, focusing on Taylor polynomials and Jacobian matrices.

Development of Taylor Polynomials

Covers the development of Taylor polynomials of order p around a point x.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Taylor Approximation: Understanding the Basics

Explores Taylor approximation for function approximation and error control.

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.