Lectures related to Functions: Multivariable Functions and Exact Differentials

Multivariable Functions: Partial Derivatives and Exact Differentials

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

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

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Mathematical Tools in Thermodynamics

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

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.

Geometric Interpretation of Derivatives

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

Partial and Total Derivatives

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

Differentiability and Tangent Planes in Multivariable Functions

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

Maxwell's Relations: Thermodynamics

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

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Partial Derivatives: Definitions and Interpretations

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

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.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Directional Derivatives and Tangent Planes

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