1. Arithmetic expressions containing Mathematical functions

2. Scientific calculations often involve Mathematical functions, such as sin, cos, tan, log, and so on. Examples: sin and ln functions on a calculator

3. 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

4. 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

5. 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

6. 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

7. Java's function library The documentation of the functions are online at the following website: http://download.oracle.com/javase/6/docs/api/inde x.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

8. Java's Mathematical functions Here are some of the names of Java's Mathematical functions:

9. Using Java's Mathematical functions Example: compute √2 Math.sqrt(2.0) = √2

10. 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

11. 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 }

12. A note on "computing values" in a computer program (cont.) Interesting result: When you compile and run this program, you will see.... absolutely nothing !!!

13. 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

14. 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 !!!

15. 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 !! } }

16. 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

17. 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 }

18. A real-life example: programming the a,b,c-formula Quadratic equation: Solutions: x 1 = x 2 =

19. 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)

20. 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);

21. 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); }

22. 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