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 |
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