Lecture

Numerical Differentiation: Methods and Errors

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In course

MATH-251(d): Numerical analysis

This course offers an introduction to numerical methods for the solution of mathematical problems as: solution of systems of linear and non-linear equations, functions approximation, integration and differentiation and solution of differential equations. ...

Description

This lecture covers numerical differentiation methods, including constructing derivatives from interpolating polynomials using linear and quadratic interpolation. It also discusses round-off errors in computer computations, emphasizing the importance of precision in calculations.

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Instructor

Pablo Antolin Sanchez

Teaching & PhD PhD Students Philipp Christoph Weder, Davor Dobrota Past EPFL PhD Students as codirector Ondine Chanon Courses Analysis III MATH-202(c) The course studies the fundamental concepts of vector analysis and Fourier-Laplace analysis with a view to their use in solving multidisciplinary problems in scientific engineering. Analysis III (for IC) MATH-203(d) The course studies the fundamental concepts of vector analysis and Fourier-Laplace analysis with a view to thei

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Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

Probabilistic numerics

Probabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.

European integration

European integration is the process of industrial, economic, political, legal, social, and cultural integration of states wholly or partially in Europe or nearby. European integration has primarily come about through the European Union and its policies. In antiquity, the Roman Empire brought about integration of multiple European and Mediterranean territories. The numerous subsequent claims of succession of the Roman Empire, even the iterations of the Classical Empire and its ancient peoples, have occasionally been reinterpreted in the light of post-1950 European integration as providing inspiration and historical precedents.

Integration by parts

In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found. The rule can be thought of as an integral version of the product rule of differentiation.

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