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Numerical methods

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Numerical methods

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A resume about numerical methods

Creada por

LAURA ALEJANDRA AVILA SUAREZ
LAURA ALEJANDRA AVILA SUAREZ
Colombia

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Numerical methodsVersión en línea

A resume about numerical methods

por LAURA ALEJANDRA AVILA SUAREZ
1

divided value independent handling curves identifying linear computer Regression interpolation nonlinearities optimization area methods relatively analytical numerical 1940s design interconnected

Since the late the widespread availability of digital computers has led to a veritable explosion in the use and development of . At fi rst , this growth was somewhat limited by the cost of access to large mainframe computers , and , consequently , many engineers continued to use simple approaches in a significant portion of their work . Needless to say , the recent evolution of inexpensive personal computers has given us ready access to powerful computational capabilities . There are several additional reasons why you should study numerical methods :
1 . Numerical methods are extremely powerful problem - solving tools . They are capable of large systems of equations , , and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically . As such , they greatly enhance your problem - solving skills .
2 . During your careers , you may often have occasion to use commercially available prepackaged , or " canned , " programs that involve numerical methods . The intelligent use of these programs is often predicated on knowledge of the basic theory underlying the methods .
3 . Many problems cannot be approached using canned programs . If you are conversant with numerical methods and are adept at computer programming , you can your own programs to solve problems without having to buy or commission expensive software .

As summarized , these are
1 . Roots of Equations . These problems are concerned with the of
a variable or a parameter that satisfies a single nonlinear equation . These problems are especially valuable in engineering design contexts where it is often impossible to explicitly solve design equations for parameters .
2 . Systems of Linear Algebraic Equations . These problems are similar in spirit to roots of equations in the sense that they are concerned with values that satisfy equations . However , in contrast to satisfying a single equation , a set of values is sought that simultaneously satisfi es a set of algebraic equations . Such equations arise in a variety of problem contexts and in all disciplines of engineering . In particular , they originate in the mathematical modeling of large systems of elements such as structures , electric circuits , and fluid networks . However , they are also encountered in other areas of numerical methods such as curve fitting and differential equations .
3 . Optimization . These problems involve determining a value or values
of an variable that correspond to a " best " or optimal value of a function . Thus , optimization involves maxima and minima . Such problems occur routinely in engineering design contexts . They also arise in a number of other numerical methods . We address both single - and multi - variable unconstrained optimization . We also describe constrained with particular emphasis on linear programming .
4 . Curve Fitting . You will often have occasion to fi t to data points . The techniques developed for this purpose can be into two general categories : regression and interpolation . is employed where there is a signifi cant degree of error associated with the data . Experimental results are often of this kind . For these situations , the strategy is to derive a single curve that represents the general trend of the data without necessarily matching any individual points . In contrast , is used where the objective is to determine intermediate values between error - free data points . Such is usually the case for tabulated information . For these situations , the strategy is to fit a curve directly through the data points and use the curve to predict the intermediate values .
5 . Integration . As depicted , a physical interpretation of numerical
integration is the determination of the under a curve . Integration has many applications in engineering practice .