Lectures related to Taylor Series: Basics and Applications

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

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

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

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

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

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

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

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

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

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

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

Provides solutions to an Analysis I exam, covering various topics.

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

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

Introduces mathematical notations and functions essential for general physics.

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