Arithmetic expressions containing Mathematical functions

1. Arithmetic expressions containing Mathematical functions

2. 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

3. Arithmetic expressions containing Mathematical functions (cont.) • Programming languages allow you to embedMathematical 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 xsin(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/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

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 variableSystem.out.println(a); // You can print the saved value later } }

18. A real-life example: programming the a,b,c-formula • Quadratic equation: • Solutions: x1 = x2 =

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