Lectures related to Taylor Series: Derivatives and Approximations

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

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Covers the concept of developing limited functions and includes physical examples.

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

Explores the corollary of Taylor's formula for function approximation around a point.

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

Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Explores developing limits using Taylor series for function approximations and understanding functions with derivatives approaching zero.

Introduces higher derivatives and the Taylor development, illustrating examples and discussing the uniqueness of the Taylor polynomial.

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

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

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

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Covers the Taylor formula and limit development for functions with multiple derivatives.

Explores limited and Taylor formulas for derivatives around specific points.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.