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Resumen del manual
To interrupt a simplification process that is taking too long, press .. You can then try simplifying only a portion of the expression. (Auto-paste the entire expression on the entry line, and then delete the unwanted parts.) Symbolic Manipulation Del DelDelDelDela aaaay yyyye eeeed Sim d Simd Simd Simd Simp ppppl lllli iiiifica ficaficaficafication f tion ftion ftion ftion fo oooor Ce r Cer Cer Cer Cer rrrrt ttttain Buil ain Builain Builain Builain Built- t-t-t-t-In Functions In FunctionsIn FunctionsIn FunctionsIn Functions Usually, variables are automatically simplified to their lowest possible level before they are passed to a function. For certain functions, however, complete simplification is delayed until after the function is performed. Fun FunFunFunFunctions ctionsctionsctionsctions tha thathathathat tttt Use UseUseUseUse Delay DelayDelayDelayDelaye eeeed Simp d Simpd Simpd Simpd Simplific lificlificlificlifica aaaation tiontiontiontion Functions that use delayed simplification have a required var argument that performs the function with respect to a variable. These functions have at least two arguments with the general form: function(expression, var [, ... ]) Note: Not all functions that use a var argument use delayed simplification. For example: solve(x^2NxN2=0,x) d(x^2NxN2,x) ‰(x^2NxN2,x) limit(x2NxN2,x,5) For a function that uses delayed simplification: 1. The var variable is simplified to the lowest level at which it remains a variable (even if it could be further simplified to a non-variable value). 2. The function is performed using the variable. 3. If var can be further simplified, that value is then substituted into the result. Symbolic Manipulation Note: You may or may not want to define a numeric value for var, depending on the situation. For example: x cannot be simplified. x is not simplified. The function uses x3, and then substitutes 5 for x. Note: The example to the right finds the derivative of x3 at x=5. If x3 was initially simplified to 75, you would find the derivative of 75, which is not what you want. x is simplified to t. The function uses t3. x is simplified to t. The function uses t3, and then substitutes 5 for t. Symbolic Manipulation Substi SubstiSubstiSubstiSubstituting V tuting Vtuting Vtuting Vtuting Va aaaalues and Setting Constr lues and Setting Constrlues and Setting Constrlues and Setting Constrlues and Setting Constrai aiaiaiaints ntsntsntsnts The “with” operator ( | ) lets you temporarily substitute values into an expression or specify domain constraints. T TTTTy yyyyp ppppi iiiin nnnng gggg t tttthe “W he “Whe “Whe “Whe “With” Oper ith” Operith” Operith” Operith” Opera aaaat ttttor orororor To type the “with” operator ( | ), press: @ I Sub SubSubSubSubs sssstit tittittittitu uuuuting f ting fting fting fting fo oooor a V r a Vr a Vr a Vr a Va aaaaria riariariariab bbbble lelelele For every occurrence of a specified variable, you can substitute a numeric value or an expression. First derivative of x3 at x = 5 To substitute for multiple variables at the same time, use the Boolean and operator. Symbolic Manipulation Sub SubSubSubSubs sssstit tittittittitu uuuuting f ting fting fting fting fo oooor a Simple Exp r a Simple Expr a Simple Expr a Simple Expr a Simple Expr rrrre eeeession ssionssionssionssion For every occurrence of a simple expression, you can substitute a variable, numeric value, or another expression. By replacing a commonly used (or long) term, you can display results in a more compact form. Note: acos(x) is different from a*cos(x). Sub SubSubSubSubs sssstit tittittittitu uuuuting Comple ting Completing Completing Completing Complex xxxx V VVVVa aaaalues lueslueslueslues You can substitute complex values just as you would for other values. Substituting s for sin(x) shows that the expression is a polynomial in terms of sin(x). All undefined variables are treated as real numbers in symbolic calculations. To perform complex symbolic analysis, you must define a complex variable. For example: x+yi!z Then you can use z as a complex variable. You can also use z_. For more information see the _ (underscore) topic in the Technical Reference module. Symbolic Manipulation Note: • For an overview of complex numbers, refer to the Technical Reference module. • To get the complex i, press 2). Do not simply type the letter i on the keyboard. Be BeBeBeBe Aw AwAwAwAwar arararare of the Limita e of the Limitae of the Limitae of the Limitae of the Limitations of Sub tions of Subtions of Subtions of Subtions of Subs sssstitu titutitutitutitutions tionstionstionstions • Substitution occurs only where there is an exact match for the substitution. substitution in simpler terms for a more complete substitution. Only x2 was replaced, not x4 . Define the Symbolic Manipulation • Infinite recursions can occur when you define a substitution variable in terms of itself. Substitutes sin(x+1), sin(x+1+1), sin(x+1+1+1), etc sin(x)|x=x+1 When you enter a substitution that causes an infi...