2. Tutorial lessons

MATLAB offers many predefined mathematical functions for technical computing which contains a large set of mathematical functions.

Typing help elfun and help specfun calls up full lists of elementary and special functions respectively.

There is a long list of mathematical functions that are built into MATLAB. These functions are called built-ins. Many standard mathematical functions, such as sin(x), cos(x), tan(x), e^x, ln(x), are evaluated by the functions sin, cos, tan, exp, and log respectively in MATLAB.

In MATLAB, there are many built-in mathematical functions that you can use for calculations. These functions save you time by eliminating the need to write the mathematical formulas from scratch. For example, if you need to calculate the sine of an angle, instead of calculating it manually using a formula, you can use the built-in function sin(). You can list all available functions in MATLAB for standard operations by typing help elfun for elementary functions and help specfun for special functions in the MATLAB command window.

Think of the built-in functions like tools in a toolbox. Just as you would grab a hammer instead of trying to create one yourself every time you need to drive a nail, you use these predefined functions instead of trying to compute sine or logarithm using basic principles each time.

Table 2.1 lists some commonly used functions, where variables x and y can be numbers, vectors, or matrices.

Apart from elementary functions, MATLAB includes predefined constant values such as pi and the imaginary unit i.

MATLAB provides a variety of functions to handle different mathematical operations. For example, sin(x) computes the sine of x, cos(x) finds the cosine, and exp(x) gives the exponential of x. You can see that x and y, which can represent numbers or collections of numbers (like arrays), are the input values for these functions. Additionally, MATLAB has certain constants like pi, which is important in various calculations, especially those involving circles and trigonometry.

Imagine you're a chef using a recipe. Just as a recipe tells you exactly what to do with certain ingredients at specific steps, MATLAB functions take well-defined inputs and output results based on mathematical rules.

We illustrate here some typical examples which relate to the elementary functions previously defined.

As a first example, the value of the expression y = e^(-a) * sin(x) + 10√y, for a = 5, x = 2, and y = 8 is computed by:

a = 5; x = 2; y = 8;
y = exp(-a)*sin(x)+10*sqrt(y)
y = 28.2904

Let's look at an example calculation in MATLAB. We define three variables: a, x, and y. We then use the exponential function exp() to compute e raised to the power of -5, and the sine function sin() to compute the sine of 2. The entire operation combines these results with additional calculations to produce a final value for y which is 28.2904. This demonstrates how you can chain functions and operations together to perform complex calculations.

Think of it like following a multi-step mathematical operation on a recipe. Just like measuring ingredients in a recipe (you might measure flour, sugar, and butter), here, we’re using specific mathematical functions on chosen values to get our final dish—or in this case, the value of y.

Note the difference between the natural logarithm log(x) and the decimal logarithm (base 10) log10(x).

To calculate sin(π/4) and e^10, we enter the following commands in MATLAB:

sin(pi/4)
ans = 0.7071

exp(10)
ans = 2.2026e+004

In this chunk, we learn that there are different types of logarithms: the natural logarithm (log()) which uses base e, and the common logarithm (log10()) which uses base 10. Knowing this distinction is important in mathematics and engineering contexts. Additionally, we can see that when calculating sin(pi/4) in MATLAB, we get a specific output, and using exp(10) gives a very large number because it computes e raised to the power of 10.

Imagine you are measuring distances on a map. The natural logarithm could be seen as measuring distances in a natural landscape, while the decimal logarithm measures road distances—both getting you somewhere different but through different paths, just like base e and base 10 logarithms lead to different results.

--