Lectures related to Newton's Method: Convergence and Conditions

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.

Explains Newton's method of order 2 for finding function zeros.

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

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

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

Explores generalized integrals, convergence, implicit functions, and higher-order derivatives.

Explores distribution interpolation spaces, convergence of sequences, derivatives, weak derivatives, and their applications in minimization problems.

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

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Explores derivability, continuity, and composite functions with illustrative examples.

Explores linear response for chaotic systems, discussing SRB states, Lyapunov exponents, and convergence of the response formula.

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

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

Explains the Jacobian matrix and derivative of composite functions with examples.

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

Covers the computation of derivatives and the properties of differentiable functions.

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Explains partial derivatives, Hessienne matrix, and their properties.

Covers variable bounds, convergence of integrals, and homomorphisms in advanced analysis.