Lectures related to Numerical Derivatives: First Order, Backward Finite Difference Formulas

Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Introduces numerical optimization with Scipy, covering zero finding, problem dimensionality, derivatives, and advanced visualization techniques.

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

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Explores the stability analysis of finite difference methods for solving differential equations.

Covers the theory of finite differences and the mean value theorem.

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Introduces numerical root finding, differentiation, integration, and ODE solving using Scipy.

Covers the concept of numerical derivative and the progressive difference approach for computing derivatives.

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

Covers the definition of derivative, examples, Newton's quotient, and continuity.

Explores numerical differentiation using finite differences and addresses the impact of errors in computer computations.

Covers the concept of numerical derivatives of order 1 and the importance of choosing a small fixed value for h.

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

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

Covers the optimization of energy systems, focusing on solving equations and numerical methods.

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Explores Runge-Kutta methods to estimate functions at multiple points for improved error estimation.