Partial Derivatives: Understanding and Applications

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Multivariable Functions: Partial Derivatives and Exact Differentials

Explores expressing oscillations as functions of time and discusses exact differentials in thermodynamics.

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.

Partial Derivatives: Higher Order and Applications

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Derivable Functions: Partial Derivatives and Jacobian Matrix

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

Directional Derivatives and Tangent Planes

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

Partial Derivatives: Derivability

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

Partial Derivatives: Matrices and Local Extrema

Covers hessian matrices, positive definite matrices, and local extrema of functions.

Partial Derivatives and Differential Equations

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

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.