3 User-Created Functions, Repetitive Operations, and Conditionals

3.1 Introduction

In this chapter, we shall introduce several ways to create functions, exercise program control by using If and Which, and perform repetitive operations by using Do, While, Nest, and Map.

There are several reasons to create functions: avoid duplicate code; limit the effect of changes to specific sections of a program; reduce the apparent complexity of the overall program by making it more readable and manageable; isolate complex operations; and perhaps make debugging and error isolation easier.

3.2 Expressions and Procedures as Functions

3.2.1 Introduction

An expression is any legitimate combination of Mathematica objects such as a mathematical formula, a list, a graphical entity, or a built-in function. Mathematica evaluates each expression in any of several ways; for example, by computing the expression (1 + 2 → 3), by simplifying it (a − 4a + 2 → 2 − 3a), or by executing a definition (r = 7 → 7). During the evaluation process, an attempt is made by Mathematica to reduce expressions to a standard form.

A procedure is a sequence of expressions to be evaluated. When this procedure is used once, it can appear within one cell and be evaluated after all the expressions have been entered or it can be evaluated on an expression-by-expression basis. However, when a procedure will be used more than once or it will be used by a built-in function, it is better to create a special object called a function. ...

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