Lectures related to Multivariable Functions: Partial Derivatives and Exact Differentials

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

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.

Thermodynamics: State, Quantities, and Differential

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

Thermodynamic Equilibrium and Mechanical Transfer

Explores mechanical equilibrium, entropy, and irreversible processes in thermodynamics.

Partial Derivatives: Definitions and Interpretations

Explores partial derivatives, their interpretations, and geometric applications in multivariable functions.

Chemical Equilibrium and Matter Transfer

Explores chemical equilibrium, matter transfer, entropy, and irreversible processes in a thermodynamic context.

Thermodynamics: Principles and Applications

Provides an overview of thermodynamic principles, focusing on the first principle and its applications in various systems.

Thermodynamic Transformations: Internal Energy and Kinetic Gas Theory

Explores thermodynamic transformations, internal energy, kinetic gas theory, and temperature measurement methods.

Functions with Multiple Variables

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

Partial Derivatives

Covers the concept of partial derivatives and properties of saddle points.

Partial Derivatives and Matrix Hessians

Covers partial derivatives, Hessian matrices, and their importance for functions with multiple variables.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.