Lectures related to Immediate Consequences

Discusses conditions for functions to be strictly increasing or decreasing based on the derivative.

Covers the concepts of increasing and decreasing functions and the relationship between the derivative and monotonicity.

Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

Tangent to Graph of a Function

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

Differential Calculus: Definition and Derivability

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

Demonstration of Theorem 8.2

Explores the conditions for a function to be continuous and differentiable.

Derivatives: Definition and Properties

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

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Convexity and Concavity

Covers the concepts of convexity and concavity in functions with examples.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Derivability and Continuity

Explores derivability, continuity, and composite functions with illustrative examples.

Change of Coordinates: Invertible Matrices & Functions

Explores invertible matrices, injective functions, and the theory of reciprocal functions.

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Concavity and Convexity: Analysis of Functions

Explores concavity, convexity, critical points, and singularities in functions.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Convexity Study and Limiting Developments

Explores convexity, concavity, and limiting developments for functions, emphasizing extrema and derivative properties.

Jacobian Matrix: Derivative of Composite Functions

Explains the Jacobian matrix and derivative of composite functions with examples.

Derivatives and Tangent Planes

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

Functions Reciprocal and Monotone: Advanced Analysis II

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.