Derivative: Linear Approximation

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Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Limits and Derivatives in Multivariable Functions

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

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Taylor Series: Derivatives and Approximations

Explores Taylor series, derivatives, and approximations in mathematical analysis.

Differential Calculation: Hyperbolic Functions

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Taylor Series: Expansion and Properties

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

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Generalized Finite Increments

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.