arithmetic expressions containing mathematical functions
DESCRIPTION
Arithmetic expressions containing Mathematical functions. Arithmetic expressions containing Mathematical functions. Scientific calculations often involve Mathematical functions , such as sin , cos , tan , log , and so on. Examples: sin and ln functions on a calculator. - PowerPoint PPT PresentationTRANSCRIPT
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Arithmetic expressions containing Mathematical functions
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Arithmetic expressions containing Mathematical functions
• Scientific calculations often involve Mathematical functions, such as sin, cos, tan, log, and so on.
Examples: sin and ln functions on a calculator
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Arithmetic expressions containing Mathematical functions (cont.)
• Programming languages allow you to embed Mathematical functions within a arithmetic expression.
Furthermore, a computer allows you to use variables are arguments to a Mathematical function
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Arithmetic expressions containing Mathematical functions (cont.)
• In other words:
• Suppose you have define a variable x as follows:
• You can write expressions like these:
double x = 2.0;
sin(x) computes the sin of x sin(2*x) computes the sin of 2*x
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Arithmetic expressions containing Mathematical functions (cont.)
• Note:
• The names of the sin, cos, tan, ln, and other Mathematical functions in Java is a little bit different than what you are used to.
• They are given below
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Java's function library
• The Java programming language has an extensive collection of functions organized in various libraries
Note: a bit of history
• In Mathematics, the sin() operation is called a function
• In Java, the sin() operation is implemented by a Java method
• In fact, we used the words "function" and "method" interchangeably in Computer Science.
• Before the word method became popular, other words used were: subroutine, procedure and function
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Java's function library
• The documentation of the functions are online at the following website:
http://download.oracle.com/javase/6/docs/api/index.html
• We will now look at the Mathematical functions which are documented on this webpage:
http://download.oracle.com/javase/6/docs/api/java/lang/Math.html
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Java's Mathematical functions
• Here are some of the names of Java's Mathematical functions:
Java's method name Corresponding Mathematical functionMath.sin(x) Sine function of value xMath.cos(x) Cosine function of value xMath.tan(x) Tangent function of value x Math.asin(x) Arc sine (inverse of sine) function of value xMath.acos(x) Arc cosine function of value x Math.atan(x) Acr tangent function of value x
Math.exp(x) ex
Math.log(x) Natural log function of value xMath.log10(x) 10-based log function of value x
Math.pow(a, b) ab
Math.sqrt(x) Squared root of the number x
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Using Java's Mathematical functions
• Example: compute √2
Math.sqrt(2.0) = √2
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Using Java's Mathematical functions (cont.)
• You can apply a Mathematical function on a floating point variable
Examples: double a;
Math.sqrt(a)
Math.sqrt(a+1)
will compute the squared root on the value that is current stored in the variable a
will compute the squared root
on the value a+1
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A note on "computing values" in a computer program
• We just learned how to compute √2
Consider the following Java program:
public class CompVal
{
public static void main(String[] args)
{
Math.sqrt(2.0); // Computes √2
}
}
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A note on "computing values" in a computer program (cont.)
• Interesting result:
• When you compile and run this program, you will see .... absolutely nothing !!!
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A note on "computing values" in a computer program (cont.)
• Example Program (Demo above code)– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/CompVal.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac CompVal.java
• To run: java CompVal
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A note on "computing values" in a computer program (cont.)
• The reason is:
• Unlike a calculator that always shows the result of a computation on its display....
A computer will only show the result of a computation when it is told !!!
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A note on "computing values" in a computer program (cont.)
• Example:
This program will print: 1.4142135623730951 (which is the decimal value of √2)
public class CompVal2
{
public static void main(String[] args)
{
System.out.println( Math.sqrt(2.0) ); // Print !! }
}
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A note on "computing values" in a computer program (cont.)
• Programming facts:
• A computed value is not printed
If you want to print a computed value, use a print statement
•A computed value is not stored
If you want to store (save) a computed value, use an assignment statement
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A note on "computing values" in a computer program (cont.)
• Example: storing a computed value
public class CompVal3
{
public static void main(String[] args)
{
double a;
a = Math.sqrt(2.0); // Save computed value in variable System.out.println(a); // You can print the saved value later
}
}
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A real-life example: programming the a,b,c-formula
• Quadratic equation:
• Solutions:
x1 = x2 =
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A real-life example: programming the a,b,c-formula (cont.)
• The Mathematical expressions are written in Java as follows:
written as:
( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a)
written as:
( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a)
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A real-life example: programming the a,b,c-formula (cont.)
• Here is a Java program to compute the famous a,b,c-formula:
public class Abc
{
public static void main(String[] args)
{
double a, b, c, x1, x2; // Define 5 variable
a = 1.0;
b = 0.0;
c = -4.0;
x1 = ( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a);
x2 = ( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a);
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A real-life example: programming the a,b,c-formula (cont.)
System.out.print("a = ");
System.out.println(a);
System.out.print("b = ");
System.out.println(b);
System.out.print("c = ");
System.out.println(c);
System.out.print("x1 = ");
System.out.println(x1);
System.out.print("x2 = ");
System.out.println(x2);
}
}
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A real-life example: programming the a,b,c-formula (cont.)
• Example Program: (Demo above code) – Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/Abc.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac Abc.java
• To run: java Abc