Defining Scalar Variables

 

A variable is a name made of a letter or a combination of several letters (and digits) that is assigned a numerical value. Name of variables must begin with a letter. After the first letter, any number of digits or underscores may be used.

Rules About Variable Name
· Variable name can be up to 31 characters long.
· Can contain letters, digits, and the underscore character.
· Must begin with a letter.
· MATLAB is case sensitive; it distinguishes between uppercase and lowercase letters. For example, FF, Ff, fF, and ff are the names of four different variables.
· Avoid using the names of a built-in function for a variable (i.e. avoid using: sin, tan, exp, sqrt, etc.)

Predefined Variables
A number of frequently used variables are already defined when MATLAB is started. Some of the predefined variables are:



Table : predefined Variables

Predefined Variables	Description
ans	A variable that has the last expression that was not assigned to a specific variable. If the user does not assign the value of an expression to a variable, MATLAB automatically stores the result in ans.
pi	The π number, π = 3.14159
eps	The smallest difference between two numbers. Equal to 2^(-52), which is approximately 2.2204e-016.
inf	Used for infinity.
i	Imaginary unit, defined as , which is 0+1.0000i.
j	Same as i.
NaN	Stands for Not a number. Used when MATLAB cannot determine a valid numeric value. For example 0/0.

Scalar mathematics with MATLAB notations

Scalar mathematics involves operations on single-valued variables. Matlab provides support for scalar mathematics similar to that provided by a calculator.

Arithmetic Operation with Scalars
The symbols of arithmetic operations are:
Table: Arithmetic Operators

Operation	MATLAB Symbol	Algebraic form	Matlab form	Example
Addition	+	a + b	a + b	7+3=10
Subtraction	-	a − b	a – b	7-3=4
Multiplication	*	a × b	a * b	7*3=21
Left-division	\	b ÷ a	a \ b	7\3=0.4286
Right-division	/	a ÷ b	a / b	7/3=2.33
Exponentiation	^	ab	a ^ b	7^3 (means 7^3= 343)

Order of Precedence
MATLAB executes the calculations according to the order of precedence displayed below. This order is the same as used in most calculators.
Table: Order of Precedence

Precedence	Mathematical Operation
First	Parenthess. For nested parenthess, the innermost are executed first.
Second	Exponentiation.
Third	Multiplication, division (Equal precedence).
Fourth	Addition and subtraction

Numeric Display Formats
MATLAB by default displays only 4 decimals in the result of the calculations, However, MATLAB does numerical calculations in double precision, which is 15 digits.

Table: Display Format

Command	Description	Example
format short	Fixed-point with 4 decimal digits for: 0.001≤number≤1000 Otherwise display format short e	>> x=250/7; >> format short >> x x = 35.7143
format long	Fixed-point with 15 decimal digits for: 0.001≤number≤100 Otherwise display format long e	>> x=250/7; >> format long >> x x = 35.714285714285715
format short e	Scientific notation with 4 decimal digits.	>> x=250/7; >> format short e >> x x = 3.5714e+001
format long e	Scientific notation with 15 decimal digits.	>> x=250/7; >> format long e >> x x = 3.571428571428572e+001
format short g	Best of 5-digit fixed or floating point.	>> x=250/7; >> format short g >> x x = 35.714
format long g	Best of 15-digit fixed or floating point.	>> x=250/7; >> format long g >> x x = 35.7142857142857
format bank	Two decimal digits.	>> x=250/7; >> format bank >> x x = 35.71
format compact	Suppresses many of the blank lines that appear in the output.
format loose	Adds empty lines (opposite of compact)

Note: If the largest element of a matrix is larger than 10³ or smaller than 10^-3, MATLAB applies a common scale factor for the short and long formats.
Elementary Math Built-in Function
Lists of some commonly used elementary MATLAB mathematical built-in functions are given in TABLES.

Table: Elementary Math Functions

Function	Description	Example
sqrt(x)	Square root; x.	>> sqrt(81) ans = 9
exp(x)	Exponential; ex.	>> exp(3) ans = 20.0855
log(x)	Natural logarithm; ln(x).	>> log(200) ans = 5.2983
log10(x)	Common (base 10) logarithm; log(x)= log10(x).	>> log10(400) ans = 2.6021
abs(x)	Absolute value.	>> abs(-27) ans = 27
factorial (x)	The factorial function x! (x must be a positive integer.)	>> factorial(4) ans = 24

Trigonometric Math Functions:
Table : Trigonometric Math Functions

Function	Description	Example
sin(x)	Sine; sin(x). (x in radians)	>> sin(pi/6) ans = 0.5000
cos(x)	Cosine; cos(x). (x in radians)	>> cos(pi/6) ans = 0.8660
tan(x)	Tangent; tan(x). (x in radians)	>> tan(pi/6) ans = 0.5774
cot(x)	Cotangent; cot(x). (x in radians)	>> cot(pi/6) ans = 1.7321
sec(x)	Secant; sec(x). (x in radians)	>> sec(pi/6) ans = 1.1547
csc(x)	Cosecant; csc(x). (x in radians)	>> csc(pi/6) ans = 2.0000
asin(x)	Inverse sine; sin–1 (x).	>> asin(1) ans = 1.5708
acos(x)	Inverse cosine; cos–1 (x).	>> acos(.5) ans = 1.0472
atan(x)	Inverse tangent; tan –1 (x).	>> atan(.5) ans = 0.4636
acot(x)	Inverse cotangent; cot –1(x).	>> acot(.5) ans = 1.1071
asec(x)	Inverse secant; sec –1 (x).	>> asec(.5) ans = 0 + 1.3170i
acsc(x)	Inverse cosecant; csc –1 (x).	>> acsc(.2) ans = 1.5708 - 2.2924i

NOTE: Trigonometric functions are sind(x), cosd(x), tand(x) and others, in which x is in degree.
Table: Hyperbolic Functions

Function	Description
cosh(x)	Hyperbolic cosine; cosh(x).
coth(x)	Hyperbolic cotangent; cosh(x)/sinh(x).
csch(x)	Hyperbolic cosecant; 1/sinh(x).
sech(x)	Hyperbolic secant; 1/cosh(x).
sinh(x)	Hyperbolic sine; sinh(x).
tanh(x)	Hyperbolic tangent; sinh(x)/cosh(x).

Rounding Functions
Table: Rounding Functions

Function	Description	Example
Round(x)	Rounds towards the nearest integer.	>> round(17/3) ans = 6
fix(x)	Rounds to the nearest integer toward zero.	>> fix(13/5) ans = 2
ceil(x)	Rounds to the nearest integer toward +∞.	>> ceil(9/5) ans = 2
floor(x)	Rounds to the nearest integer toward - ∞.	>> floor(-9/5) ans = -2
sign(x)	Signum function. Returns 1 if x>0, -1 if x<0, and 0 if x=0.	>> sign(7) ans = 1
rem(x,y)	Returns the remainder after x is divided by y.	>> rem(9,5) ans = 4