Derivability and Limits in Analysis I

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Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivatives: Definition and Properties

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

Differentiability of Functions of Several Variables

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

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Linear Approximation and Derivative Parametric

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

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Differentiability and Tangent Planes in Multivariable Functions

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

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Optimality Conditions: Unconstrained

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

Differentiability and Derivatives

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.