Learning Euler's Method for Differential Equations

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SUMMARY

This discussion focuses on learning Euler's Method for solving differential equations, particularly using a TI-84 calculator and spreadsheet software like Excel. Participants highlight the importance of using small step sizes (dx) for improved accuracy in numerical solutions. While exact solutions are not achievable with numerical methods, users can control the precision of their results by adjusting step sizes and employing better techniques. The conversation emphasizes the balance between approximation and the desired level of accuracy in mathematical computations.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with Euler's Method
  • Basic knowledge of using TI-84 calculators
  • Experience with spreadsheet software like Excel
NEXT STEPS
  • Research how to implement Euler's Method on a TI-84 calculator
  • Learn to use Excel for numerical methods in calculus
  • Explore the concept of step size (dx) in numerical analysis
  • Investigate alternative numerical methods for solving differential equations
USEFUL FOR

Students learning calculus, educators teaching differential equations, and anyone interested in numerical methods for approximating solutions to mathematical problems.

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We just started learning how to find diffrencial equations using the eulers method. I heard there is a programm in a calculator that let's you do that. I have a ti 84 I don't know the name of the program if you can be kind and give me the website it would be appreciated. My calculus book had this question in which you have to find a point given the intial condition with dx like .05. Crazy!
I was also wondering if you could use spreadsheet to plot and find the diffrencial equation easly.
One more question :-p
Can you find the exact solution if your dx approched 0 and is it possible to find an exact answer.
Thanks for the help!
 
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I have no idea about your TI, try reading the manual.

Euler's method is a very simple method which works very well in Excel. The trouble is you have to take VERY small steps to get good results.

As far as exact answer goes it depends on what you mean by exact answer. Numeric methods yield an approximate solution, however you have control over the number of "good" digits. Small step size and/or better methods yield better results. You can always get as many digits as you need. Is that exact?
 

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