Numerical Analysis: A Textbook for Beginning Numerical Methods

Overview

Numerical analysis is the study of algorithms for solving problems that cannot be solved analytically. Numerical methods are used in a wide variety of fields, including:

Numerical Analysis

by J. Douglas Faires

4.3 out of 5

Language	:	English
File size	:	26388 KB
Screen Reader	:	Supported
Print length	:	912 pages

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* Mathematics * Science * Engineering * Business * Finance

Numerical methods are essential for solving problems that are too complex to be solved by hand, such as:

* Finding the roots of equations * Interpolating data * Integrating functions * Solving differential equations

Goals of Numerical Analysis

The goals of numerical analysis are to:

* Develop algorithms that are accurate and efficient. * Analyze the accuracy and efficiency of algorithms. * Provide software implementations of algorithms.

Topics Covered in Numerical Analysis

Numerical analysis covers a wide range of topics, including:

* Approximation * Root finding * Interpolation * Integration * Differentiation * Linear equations * Differential equations

Approximation

Approximation is the process of finding an approximate solution to a problem. Numerical methods for approximation include:

* Taylor series * Padé approximants * Continued fractions

Root Finding

Root finding is the process of finding the roots of an equation. Numerical methods for root finding include:

* Bisection method * Newton's method * Secant method

Interpolation

Interpolation is the process of finding a function that passes through a given set of data points. Numerical methods for interpolation include:

* Lagrange interpolation * Spline interpolation * Hermite interpolation

Integration

Integration is the process of finding the area under a curve. Numerical methods for integration include:

* Trapezoidal rule * Simpson's rule * Gaussian quadrature

Differentiation

Differentiation is the process of finding the derivative of a function. Numerical methods for differentiation include:

* Forward difference * Backward difference * Central difference

Linear Equations

Linear equations are equations that can be written in the form Ax = b, where A is a matrix, x is a vector, and b is a vector. Numerical methods for solving linear equations include:

* Gaussian elimination * LU decomposition * QR decomposition

Differential Equations

Differential equations are equations that involve derivatives. Numerical methods for solving differential equations include:

* Euler's method * Runge-Kutta methods * Finite difference methods

Numerical Analysis Software

There are a number of software packages available for performing numerical analysis. Some of the most popular packages include:

* MATLAB * Octave * SciPy * NumPy

These packages provide a wide range of functions for performing numerical analysis tasks.

Numerical analysis is a powerful tool for solving problems that cannot be solved analytically. Numerical methods are used in a wide variety of fields, and they are essential for solving problems that are too complex to be solved by hand.

If you are interested in learning more about numerical analysis, there are a number of resources available online. You can find textbooks, tutorials, and software packages that can help you get started.

Numerical Analysis

by J. Douglas Faires

4.3 out of 5

Language	:	English
File size	:	26388 KB
Screen Reader	:	Supported
Print length	:	912 pages

FREE