Lectures related to Mathematical Complements: df or δf

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.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and integrals, including conservative quantities and exact total differentials.

Functions: Parametric, Integrals, Multi-variable

Covers parametric functions, integrals, and the origin of plasticity in metals.

Multivariable Functions: Partial Derivatives and Exact Differentials

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

Geometric Interpretation of Derivatives

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

Functions: Differentials, Taylor Expansions, Integrals

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

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Derivatives and Continuity in Multivariable Functions

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

Surface Integrals: Change of Variables

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

Functions with Values in R^m

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

Partial Derivatives: Understanding and Applications

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

Partial Derivatives Rules

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

Partial Derivatives and Differential Equations

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

Existence and Uniqueness of Local Solutions

Explores the proof of existence and uniqueness of local solutions for a Cauchy problem with separable variables.

Advanced Analysis II: Sequences and Integrals

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

Differential Calculus: Applications and Reminders

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

Partial and Total Derivatives

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

Calculus Fundamentals

Covers the fundamentals of calculus, including limits, derivatives, and integrals.