4/9/2014 Exponential - MATLAB exp

http://www.mathworks.com/help/matlab/ref/exp.html 1/5

Exponential

Y = exp(X) example

example

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exp

Syntax

Description

Y = exp(X) returns the exponential for each element of array X. The function accepts both real and

complex inputs. For real values of X in the interval (-Inf, Inf), exp returns real values in the interval (0,Inf).

For complex values of X, exp returns complex values.

Examples

Calculate Scalar Exponential Values

Examine several common values of the exponential function.

Calculate the exponential of 0.

exp(0)

ans =

1

The result is 1, w hich is the y-intercept of the exp function.

Calculate the exponential of 1.

exp(1)

ans =

2.7183

The result is equal to Euler's number, e.

Calculate the exponential of iπ.

exp(1i*pi)

ans =

-1.0000 + 0.0000i

The result of -1 is due to Euler's famous formula

Calculate the exponential of -Inf.

exp(-Inf)

ans =

4/9/2014 Exponential - MATLAB exp

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0

The result is 0 since exp returns small values for negative inputs.

Plot Real-Valued Exponential Function

Define the domain.

X = (-1:0.5:5)';

Calculate the exponential of the vector, X.

Y = exp(X)

Y =

0.3679

0.6065

1.0000

1.6487

2.7183

4.4817

7.3891

12.1825

20.0855

33.1155

54.5982

90.0171

148.4132

The result is a vector of exponential values.

Plot the function values.

plot(X,Y,'LineWidth',1.5)

grid on;

title('Real-Valued Exponential Function');

xlabel('X'); ylabel('Y');

4/9/2014 Exponential - MATLAB exp

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The real-valued exponential function maps values in the domain of all real numbers to the range of .

Plot Complex-Valued Exponential Function

Define a grid of values for the (X,Y) domain.

[X,Y] = meshgrid(0:0.5:10,0:0.5:10);

Calculate the complex exponential on the grid.

Z = exp(X+1i*Y);

Make a surface plot of the imaginary portion of the function.

surf(X,Y,imag(Z))

grid on; hold on;

xlabel('X'); ylabel('Y'); zlabel('Z');

view(44,42)

4/9/2014 Exponential - MATLAB exp

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exp is a continuous function on the complex plane.

Plot the real portion of the function in the same figure.

surf(X,Y,real(Z))

view(63,14)

4/9/2014 Exponential - MATLAB exp

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In this plot, the real and complex portions of the function are 90 degrees out of phase. Analytically, this is because the real

portion depends on cos, w hereas the complex portion depends on sin.

Input Arguments

X — Input array

scalar | vector | matrix | multidimensional array

More About

Algorithms

For complex inputs z = x + 1i*y, the exp function calculates the complex exponential exp(x).*(cos(y) +

1i*sin(y)).

See Also

expint | expm | expm1 | log | log10 | mpower | power