Arithmetic expressions containing Mathematical functions Arithmetic expressions containing

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:

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 Comp. Val { 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/ Comp. Val. java • How to run the program: • Right click on link and save in a scratch directory • To compile: javac Comp. Val. java • To run: java Comp. Val

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 Comp. Val 2 { public static void main(String[] args) { System. out. println( Math. sqrt(2. 0) ); // Print !! } } 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 Comp. Val 3 { 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, cformula • Quadratic equation: • Solutions: x 1 = x 2 =

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, x 1, x 2; // Define 5 variable a = 1. 0; b = 0. 0; c = -4. 0; x 1 = ( -b - Math. sqrt( b*b - 4*a*c ) ) / (2*a); x 2 = ( -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("x 1 = "); System. out. println(x 1); System. out. print("x 2 = "); System. out. println(x 2); } }

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