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32nd International Conference on Technology in Collegiate Mathematics
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VIRTUAL CONFERENCE
32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
#ICTCM
VIRTUAL CONFERENCE ictcm.com | #ICTCM 32 nd International Conference - - PowerPoint PPT Presentation
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
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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ABSTRACT
- Solving a polynomial equation of degree three
- r 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.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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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
- f degree three or higher we might end up
using a numerical approximation to approximate the zero of a function.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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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.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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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.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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MAPLE CODE-1
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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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.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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MAPLE CODE-2
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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Conclusion:
- MAPLE programming with the Newton's
formula is powerful in approximating a zero of an equation where we have no established formulas.
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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE
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