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Arithmetic expressions (cont.) Using brackets: Brackets (... ) can be used to group expressions together An expression grouped by brackets (... ) is evaluated first (When brackets are nested, the inner bracketed expression is evaluated first)
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Working with floating point expressions
Arithmetic expressions
• Using the arithmetic operators:
and brackets ( ... ), we can construct arithmetic expression
• +
• −
• *
• /
Arithmetic expressions (cont.)
• Using brackets:
• Brackets ( ... ) can be used to group expressions together
• An expression grouped by brackets ( ... ) is evaluated first
(When brackets are nested, the inner bracketed expression is evaluated first)
Arithmetic expressions (cont.)
• Example: computing the average of 3 numbers
public class Average { public static void main(String[] args) { double a, b, c, avg; // Define 4 variables a = 3.0; b = 4.0; c = 6.0; avg = (a + b + c)/3.0; System.out.print("The average = "); System.out.println(avg); } }
Arithmetic expressions (cont.)
• Example Program: (Demo above code) – Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/Average.java
• How to run the program:
• Right click on link and save in a scratch directory • To compile: javac Average.java • To run: java Average
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
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
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
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
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
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
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 xMath.exp(x) ex
Math.log(x) Natural log function of value xMath.log10(x) 10-based log function of value xMath.pow(a, b) ab
Math.sqrt(x) Squared root of the number x
Using Java's Mathematical functions
• Example: compute √2
Math.sqrt(2.0) = √2
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
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 }
}
A note on "computing values" in a computer program (cont.)
• Interesting result:
• When you compile and run this program, you will see .... absolutely nothing !!!
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
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 !!!
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 !! }
}
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
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
} }
A real-life example: programming the a,b,c-formula
• Quadratic equation:
• Solutions:
x1 = x2 =
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)
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);
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);
} }
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