Lectures related to Discussion of Function f

Functions Reciprocal and Monotone: Advanced Analysis II

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

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Derivability of Reciprocal Function

Covers the derivative of the reciprocal function and its properties.

Derivatives Rules: Notation, Extrema

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Differentiability and Derivatives

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

Closed Intervals: Definitions and Remarks

Explains definitions and remarks about closed intervals in functions.

Rolle's Theorem

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

Computing Derivatives: Derivatives and Algebraic Operations

Covers the computation of derivatives and the properties of differentiable functions.

The Increment Theorem: Understanding Derivatives

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Theorem of Generalized Mean Value: Study of Functions

Explores the conditions for continuity and differentiability of functions on a closed interval.

Differential Calculus: Definition and Derivability

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

Derivatives and Function Composition

Covers derivatives rules and function composition with examples and explanations.

Derivatives and Reciprocal Functions

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

Change of Coordinates: Invertible Matrices & Functions

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Inverse Function Identity

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.