Category Archive for: Symbolic Calculation

Limits to Symbolic Processing

As you work with the symbolic processor, you will undoubtedly discover two things: • many problems can only be solved numerically, and • many more problems yield such lengthy expressions that you’ll wish you had solved them numerically. For a computer, symbolic operations are, in general, much more difficult than the corresponding numerical operations. In fact, if…

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Using Functions and Variables

Mathcad’s symbolic processor does not treat functions and variables in exactly the same way as its numerical processor. These differences revolve around the answers to the following question: • Does the symbolic processor “know” that a function or variable is defined elsewhere? The answer to this depends on two things: • Is the function or variable built-in…

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Symbolic Optimization

In general, Mathcad’s symbolic processor and Mathcad’s numerical processor don’t communicate with one another. Because of this, it’s possible to set up a complicated numerical calculation without knowing that you could have reduced it to an equivalent but much simpler problem by judicious use of the symbolic processor. You can, however, make the numerical processor ask the symbolic…

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Symbolic Transforms

This section describes how to perform the Fourier, Laplace, and z-transforms, and their inverses. The examples in this section demonstrate “live” transformations using symbolic keywords, but you may apply the Transforms commands from the Symbolics menu to expressions on a case by case basis if you prefer. Keep in mind that, unlike keyword-modified expressions, expressions modified by commands from…

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Symbolic Matrix Manipulation

This section describes how to find the symbolic transpose, inverse, and determinant of a matrix. The examples in this section demonstrate ”live” symbolic matrix manipulation using the matrix operators, described , “Vectors and Matrices,” and the symbolic equal sign. You may, however, apply the Matrix commands from the Symbolics menu to matrices on a case by case basis if…

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Solving Equations Symbolically

This section discusses how to use either keywords or menu commands from the Symbolics menu to symbolically solve an equation for a variable, find the symbolic roots of an expression, and solve a system of equations symbolically. Most of the examples in this section demonstrate “live” solving using symbolic keywords, but you may apply commands from the Symbolics menu…

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Symbolic calculus

This section describes how to symbolically evaluate definite and indefinite integrals, derivatives, and limits. Derivatives To evaluate a derivative symbolically, you can use Mathcad’s derivative operator and the live symbolic equal sign as shown in Figure 17-14: • Type? to create the derivative operator or type [Ctrl]? to create the higher order derivative operator. • In the placeholders,…

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Symbolic algebra

Mathcad allows you to manipulate an expression algebraically using either keywords and the symbolic equal sign, or menu commands from the Symbolic menu. Most of the examples in this section demonstrate “live” symbolic operations using symbolic keywords, but you may apply commands from the Symbolic menu to expressions on a case by case basis if you prefer. Keep in…

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Symbolic Calculation

What is symbolic math? Elsewhere in this User’s Guide, you’ve seen Mathcad engaging in numerical mathematics. This means that whenever you evaluate an expression, Mathcad returns one or more numbers, as shown at the top of Figure 17-1. Although these numbers are quite useful, they may provide little insight into the underlying relationship between the components in an expression.…

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Using the Symbolics menu

One advantage to using the symbolic equal sign discussed in the last section is that it is “live,” just like the numerical processing in Mathcad. That is, Mathcad checks all the variables and functions making up the expression being evaluated to see if they’ve been defined earlier in the worksheet. If Mathcad does find a definition, it uses…

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