Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Numerical Derivatives of Order 2

Description

This lecture covers the concept of numerical derivatives of order 2, including the calculation of f''(x) using limits, the approximation of f'(x) and f(x) at different points, and the error analysis involved in numerical differentiation.

In MOOC

Numerical Analysis for Engineers

Official source

Quiz

Related concepts (12)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Error analysis (mathematics)

In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics. In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean. For instance, in a system modeled as a function of two variables Error analysis deals with the propagation of the numerical errors in and (around mean values and ) to error in (around a mean ).

Approximation

An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- (ad- before p becomes ap- by assimilation) meaning to. Words like approximate, approximately and approximation are used especially in technical or scientific contexts. In everyday English, words such as roughly or around are used with a similar meaning. It is often found abbreviated as approx.

Related lectures (35)

Numerical Differentiation: Part 1

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

Numerical Differentiation: Backward and Central Differences

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

Euler Forward Method

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.

Numerical Differentiation MOOC: Numerical Analysis for Engineers

Discusses numerical differentiation, error analysis, and finite difference formulas.

Numerical Derivatives of Order 1, Rounding Errors MOOC: Numerical Analysis for Engineers