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Mathematical Complements: df or δf, Consequences
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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.