Lectures related to Implicit Examples: Hyperplane and Stationary Points

Explores finding the equation of the tangent line to a function's graph at a point.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Differential Calculation: Trigonometric Derivatives

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

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Implicit Function Theorem

Explores the Implicit Function Theorem, supporting hyperplanes, local extrema, and higher-order derivatives, concluding with the classification of stationary points.

Partial Derivatives: Taylor Formula

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

Mathematical Methods for Materials Science: Integrals, Exact Differentials

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

Points 7-9 du procédé

Covers the analysis of local and global extrema, concavity, and inflection points.

Inflection Points

Explores inflection points in functions, emphasizing the role of the second derivative.

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Implicit Function Theorem: Local Extrema

Explores the Implicit Function Theorem, local extrema, supporting hyperplanes, and higher-order derivatives.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Derivatives and Convexity

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

Derivable Functions: Partial Derivatives and Jacobian Matrix

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

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

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