Lectures related to Symmetric derivative

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Optimality Conditions: Unconstrained

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

Optimality Conditions: Sufficient Optimality Conditions

Explores the sufficient optimality conditions for local minima in functions.

Convexity and Concavity

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

Surjectivity of Derivative Application

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

Continuous Derivable Functions

Covers continuously derivable functions on open intervals with continuous derivatives and examples of different derivative orders.

Convexity and Optimization

Explores convexity, optimization, and critical points in mathematical functions using the second derivative.

Demonstration of Rolle's Theorem

Demonstrates how to use a specific function to prove Rolle's Theorem.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Rolle's Theorem and Derivatives

Covers Rolle's Theorem and derivatives, exploring their properties and applications.

Mathematical Complements: df or δf

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

Concavity and Convexity: Analysis of Functions

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

Objective function, Differentiability, The second order

Explores the role of first and second derivatives in function curvature and convexity.

Continuity and Differentiability of Functions

Covers continuity, differentiability, and applications in calculus with an emphasis on fundamental concepts.

Rolle's Theorem: Applications and Examples

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

Derivability and Limits in Analysis I

Explores derivability, limits computation, and properties of functions in Analysis I.

Inflection Points

Explores inflection points in functions, emphasizing the role of the second derivative.

Continuous Derivatives

Covers the concept of continuous derivatives and their application in analyzing functions and determining critical points.

Numerical Derivatives: First Order, Backward Finite Difference Formulas

Discusses the error between f'(x0) and its approximation using a backward finite difference formula.

Python Sets Operations

Covers Python sets operations, including creation, modification, and comparison, as well as set operations like union and intersection.