Lectures related to Taylor Polynomial: Order 2

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

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

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

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

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

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

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

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

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

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

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

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

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

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

Explains partial and directional derivatives, and functions' derivability.

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Explores solutions of differential equations and their monotonicity properties.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.