Lectures related to General Case

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

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

Differential Calculation: Trigonometric Derivatives

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

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Directional Derivatives

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

Points 7-9 du procédé

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

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Applications of Differential Calculus

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

Derivatives and Convexity

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

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Optimization: Stationary Points and Local Extrema

Covers the concept of stationary points in optimization and how to identify local extrema.

Inflection Points

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

Chapter 5: Function Studies

Covers the study of functions, including limits, derivatives, and sign variations.

Implicit Function Theorem: Local Extrema

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

Function Studies: Limits, Derivatives, and Convexity

Covers the essential elements for studying a function, including its domain, behavior at boundaries, limits, derivatives, and points of inflection.

Implicit Function Theorem

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

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.

Rolle's and Mean Value Theorem

Covers higher derivatives, local extrema, and the application of Rolle's and Mean Value Theorems.

Derivative and Local Extrema Study

Explores the study of local minima and maxima through derivatives and sign changes.

Derivatives and Reciprocal Functions

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