Lectures related to Mathematical Complements: df or δf, Consequences

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.

Geometric Interpretation of Derivatives

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

Multivariable Functions: Partial Derivatives and Exact Differentials

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

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Partial Derivatives and Differential Equations

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

Differential Functions: Definitions and Notations

Covers the definition of differentiable functions and introduces the concept of differential functions.

Derivatives and Continuity in Multivariable Functions

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

Advanced Analysis 2: Linear Differential of Functions

Explores linear differential of functions, continuity, differentiability, and matrix representation.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Partial Derivatives Rules

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

Partial Derivatives and Functions

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

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Partial Derivatives: Understanding and Applications

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

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Functions with Multiple Variables

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

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Partial and Total Derivatives

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

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.