Mathematical Tools in Thermodynamics

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Explores state, extensive and intensive quantities, differentials, processes, and temporal derivatives in thermodynamics.

Discusses thermodynamic functions, their mathematical tools, and key relationships between state variables in thermodynamics.

Covers the concept of orthogonality between vectors and the notion of distance between functions.

Explains partial derivatives, Hessienne matrix, and their properties.

Covers the definitions and relationships between calorimetric coefficients in perfect gases.

Explores phase transitions and stability criteria in thermodynamics, emphasizing entropy, internal energy, and thermodynamic potentials.

Explores differentiability in two variables and the chain rule for compositions.

Explores surface integrals, change of variables, and properties of regular surfaces.

Explores the thermodynamics of lead-acid batteries and their efficiency calculations.

Covers historical thermodynamics, continuity equations, state functions, and Cartesian products in scalar and vectorial forms.