Week 7 Engineering Concepts(1).pptx - ME 1101/L Digital Computation Patrick Mannion M.S Spring 2019 Week 7 Engineering Concepts Finding Zero’s with

# Week 7 Engineering Concepts(1).pptx - ME 1101/L Digital...

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ME 1101/L Digital Computation Week 7 Engineering Concepts Patrick Mannion, M.S. Spring 2019
Finding Zero’s with Newton’s Method
Limitation: can only evaluate function Start somewhere (guess) Draw tangent line at Y=MX+B m=Y’ which we can approximate Find lines zero i or really close then Done! If not say i=i+1 and repeat Finding Zero’s with Newton’s Method 0 10 20 30 40 50 60 -60 -40 -20 0 20 40 60 80 100 120 140 f(x) = 0.1 x² − 2 x − 30 ? ? ? = ? ? ( ? ? + 1 ? ? ) + ? ? ? ? + 1 ? ? ? ? + 1
Start somewhere (guess) Draw tangent line at Y=MX+B Y Find lines zero Repeat till Y but….. Finding Zero’s with Newton’s Method 0 10 20 30 40 50 60 -60 -40 -20 0 20 40 60 80 100 120 140 f(x) = 0.1 x² − 2 x − 30 ? 0 = 20 ? 1 = 35 ? 1 = 22.5 ? 0 = 30
Limitation: can only evaluate function Start at last guess Draw tangent line at Y=MX+B m=Y’ which we can approximate Find lines zero Repeat till but …. Finding Zero’s with Newton’s Method 0 10 20 30 40 50 60 -60 -40 -20 0 20 40 60 80 100 120 140 f(x) = 0.1 x² − 2 x − 30 ? = 5 ( ? 2 35 ) + 22.5 ? 2 = 30.5 ? 2 = 2.025 =22.5
Finding Zero’s with Newton’s Method 0 10 20 30 40 50 60 -60 -40 -20 0 20 40 60 80 100 120 140 f(x) = 0.1 x² − 2 x − 30
Euler’s Method (numerical

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