VIRTUAL CONFERENCE ictcm.com | #ICTCM 32 nd International Conference - PowerPoint PPT Presentation

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE ictcm.com | #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM MAPLE PROGAMMING IN APPROXIMATING ZEROS OF DIFFERENTIABLE FUNCTIONS WITH DESIRED ACCURACY

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM ABSTRACT • Solving a polynomial equation of degree three or higher, equations involving transcendental functions is not always easy. • We shall use either EXCEL spreadsheet or MAPLE PROGRAMMING to approximate a solution to a desired accuracy. • Here we will use MAPLE PROGRAMMING.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM DISCUSSION • Finding the zeros or roots of an equation depends on the type of the equation. • We have an already established formula for solving a quadratic equation. • If the equation is a polynomial equation of degree three or higher we might end up using a numerical approximation to approximate the zero of a function.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM NEWTON’S ITERATIVE FORMULA X(n+1)=x(n) - f(x(n))/f'(x(n)) We terminate the process when |x(n)-x(n+1)| < desired accuracy.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM EXAMPLE 1 • Use MAPLE Programming and Newton’s Iterative Formula to approximate the zero of the function f(x)=x ^3 +x-1. • Continue the process until the successive iterations differ by less than 0.001.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM MAPLE CODE-1

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Example 2 • Use MAPLE programming and Newton's Method to approximate a zero of the equation sin(x)=x^2 on (0, π/2) Continue the iterative process until two • successive iterations differ by less than 0.00001.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM MAPLE CODE-2

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Conclusion: • MAPLE programming with the Newton's formula is powerful in approximating a zero of an equation where we have no established formulas.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Contact Information Somasundaram Velummylum Professor of Mathematics Claflin University svelummylum@claflin.edu Facebook / Somasundaram Velummylum