Geometric Interpretation of Derivatives

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Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Functions with Multiple Variables

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Directional Derivatives and Tangent Planes

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Mathematical Complements: df or δf, Consequences

Explores the consequences of exact differential forms and necessary conditions for total exact differentials, using examples from mountain hiking.

Differential Calculus: Definition and Derivability

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

Partial Derivatives and Differential Equations

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

Tangent to Graph of a Function

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