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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 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: double x = 2.0; • You can write expressions like these: 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/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 Java's Mathematical functions • Here are some of the names of Java's Mathematical functions: Java's method name Math.sin(x) Math.cos(x) Math.tan(x) Math.asin(x) Math.acos(x) Math.atan(x) Math.exp(x) Math.log(x) Math.log10(x) Corresponding Mathematical function Sine function of value x Cosine function of value x Tangent function of value x Arc sine (inverse of sine) function of value x Arc cosine function of value x Acr tangent function of value x ex Natural log function of value x 10-based log function of value x Math.pow(a, b) Math.sqrt(x) a Squared root of the number x b 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: public class CompVal2 { public static void main(String[] args) { Print !! } System.out.println( Math.sqrt(2.0) ); // } This program will print: 1.4142135623730951 (which is the decimal value of √2) 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; value later } } a = Math.sqrt(2.0); // Save computed value in variable System.out.println(a); // You can print the saved A real-life example: programming the a,b,cformula • Quadratic equation: • Solutions: x1 = x2 = A real-life example: programming the a,b,cformula (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,cformula (cont.) • Here is a Java program to compute the famous a,b,cformula: 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,cformula (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,cformula (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