Lectures related to Advanced Analysis II: Derivatives and Notations

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Differentiability and Derivatives

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Mathematical Notations and Functions in General Physics

Introduces mathematical notations and functions essential for general physics.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Functional Derivatives

Covers the concept of functional derivatives and their calculation process with examples.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Differentiability and Matrices

Explores differentiability, matrices, Jacobian matrix, and derivatives calculation.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Functions of Class C^p

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.