Multivariable Functions: Partial Derivatives and Exact Differentials

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Partial Derivatives Rules

Explores rules of derivation, including partial derivatives and cyclic identities.

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.

Functions: Multivariable Functions and Exact Differentials

Explores functions as a function of time and space, differentiation of multivariable functions, exact differentials, and gradients.

Partial and Total Derivatives

Covers partial and total derivatives, differentials, and temporal derivatives in functions with multiple variables.

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.

Maxwell's Relations: Thermodynamics

Covers Maxwell's relations in thermodynamics, including internal energy, free energy, enthalpy, and Gibbs free energy.

Mathematical Tools in Thermodynamics

Covers mathematical tools used in thermodynamics and explores examples of auxiliary variables.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Derivatives and Continuity in Multivariable Functions

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

Partial Derivatives: Understanding and Applications

Explores the computation and significance of partial derivatives in determining rates of change.