Márcio Neto
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Guide to Using Mathematical Expressions with Voima Toolbox
Voima Toolbox enables you to perform a wide range of mathematical calculations using expressions using the following calculation blocks in the flowsheet editor:
 Function1
 Function2
 Function3
This guide will help you understand what types of expressions are allowed and how to use them effectively.
Basic Arithmetic Operations
Voima Toolbox supports all standard arithmetic operations, including:
 Addition:
+
(e.g.,2 + 3
results in5
)  Subtraction:

(e.g.,5  2
results in3
)  Multiplication:
*
or·
(e.g.,4 * 3
results in12
)  Division:
/
(e.g.,10 / 2
results in5
)  Exponentiation:
^
(e.g.,2 ^ 3
results in8
)
Using Variables
Variables allow you to represent numbers or results within your expressions. Voima Toolbox supports the use of variables such as x
, y
, and z
.
Example
f(x, y) = x^2 + 2*y
Here, x
and y
are variables. You can assign values to them and calculate the result based on the given expression.
Mathematical Functions
Voima Toolbox includes a wide range of builtin mathematical functions:
 Square Root:
sqrt(x)
(e.g.,sqrt(9)
results in3
)  Sine:
sin(x)
(e.g.,sin(π/2)
results in1
)  Cosine:
cos(x)
(e.g.,cos(0)
results in1
)  Tangent:
tan(x)
(e.g.,tan(π/4)
results in1
)  Logarithm:
log(x)
is the $\ln(x)$. You can also uselog(x, base)
, which gives $\log_{base}x$
Advanced Functions
For more complex calculations, Voima Toolbox also supports:
 Absolute Value:
abs(x)
(e.g.,abs(5)
results in5
)  Power:
pow(x, y)
(e.g.,pow(2, 3)
results in8
)  Exponent:
exp(x)
(e.g.,exp(1)
results ine
)
Constants
Voima Toolbox provides a set of useful constants:
 Pi:
pi
orπ
(approx.3.14159
)  Euler's Number:
e
(approx.2.71828
)
Logical and Comparison Operators
Logical and comparison operators allow you to create expressions that evaluate to true (always converted to 1) or false (always converted to 0).
 Greater Than:
>
(e.g.,x > 2
)  Less Than:
<
(e.g.,x < 5
)  Equal To:
==
(e.g.,x == 3
)  Not Equal To:
!=
(e.g.,x != 4
)  And:
&&
(e.g.,x > 2 && y < 5
)  Or:

(e.g.,x < 1  y > 3
)
Examples of Expressions
 Simple Arithmetic:
3 + 5 * 2
results in13
 Using Variables:
x^2 + y^2
forx = 3
andy = 4
results in25
 Mathematical Functions:
sqrt(x^2 + y^2)
forx = 3
andy = 4
results in5
 Logical Operations:
x > 0 && y < 10
forx = 5
andy = 3
results intrue
Common Mistakes and How to Avoid Them

Mismatched Parentheses: Always check that every opening parenthesis has a corresponding closing parenthesis.
 Example: Use
(2 + 3) * 4
instead of2 + 3 * 4)
.
 Example: Use

Undefined Variables: Ensure all variables are defined before using them in an expression.
 Example: Define
x
before usingf(x) = x^2
.
 Example: Define

Incorrect Syntax: Use the correct syntax for functions and operators.
 Example: Use
sqrt(x)
instead ofsquareRoot(x)
.
 Example: Use
By following these guidelines, you can effectively use Voima Toolbox for a wide range of mathematical calculations.