Lectures related to Derivative: Application Examples

Tangent to Graph of a Function

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

General Mathematics I: Derivatives and Tangents

Explores derivatives, tangents, and elementary function rules in general mathematics.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Rolle's Theorem: Applications and Examples

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

Partial Derivatives: Understanding Tangents

Explores partial derivatives and their role in determining tangents to graphs.

Equation of Tangent Hyperplane

Explores finding the equation of a tangent hyperplane to a function and its implications.

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Real Functions of Two Real Variables

Explores real functions of two real variables, illustrating domains, images, and graphs.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Cayley Graphs: Properties and Applications

Explores the properties and applications of Cayley graphs in group theory and network analysis.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Restriction, Prolongement et Graphe d'une Fonction

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

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Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Modular Programming: Managing Project Complexity

Covers modular programming principles, focusing on managing project complexity through effective code structuring and dependency management.

Functions and Integers

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.