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Lecture
Taylor Series: Development and Applications
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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.
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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.