Lectures related to Taylor Series: Development and Applications

Application of Taylor's approximation formula

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

Taylor's Formula: Developments and Applications

Explores Taylor's formula, polynomials, functions, and series applications.

Explores Taylor series, function properties, inflection points, and critical points in graphical and mathematical contexts.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Derivatives and Convexity

Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.

Taylor Polynomials: Special Cases

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

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Taylor's Formula: Convexity, Inflection Points

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Local Extremum Points Determination

Focuses on determining local extremum points of functions through various examples.

Integration: Taylor Approximation & Convex Functions

Covers Taylor approximation, convex functions, and integrable properties.

Convexity and Concavity: Inflection Points, Taylor Expansion, and Darboux Sums

Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Extrema of Functions

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

Explores limits, derivation rules, integrals, and exact differentials for practical applications.

Applications of Differential Calculus

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.

Functions: Differentials, Taylor Expansions, Integrals

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

Extrema of Functions in Several Variables

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.