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# taylor - (x cos(x 2 2 f(x = 2*sin(x*cos(x 2 cos(x sin(x f(x...

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Welcome to CSci 2031 - Introduction - Matlab - Taylor Series

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James Parker Office hours: Monday: 11:30am - 1:00pm Wednesday: 11:15am - 3:00pm Thursday: 10:00am - 1:00pm Email: [email protected] Room: EE/CS 2-209
Huahua Wang Office hours: TBD Email: [email protected] Room: EE/CS 2-209

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Matlab Need ITlabs account to access! www.itlabs.umn.edu
Taylor series Taylor series: f(x) ~ f(0) + x*f'(0) + x *f''(0) +x *f'''(0) + ... ~ 2 3 3! 2!

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Example: 4 2 3 2 f(0) = 8 f'(0) = 0 f''(0) = 10 f'''(0)=0 f''''(0)=72 f(x) = 3x + 5x + 8 f'(x) = 12x + 10x f''(x) = 36x + 10 f'''(x) = 72x f''''(x) = 72 Taylor series
Taylor series: f(x) ~ + x* + x * +x * + x * ~ 2 3 3! 2! f(x) = 3x + 5x +8 4 2 4 4! f(0) f''(0) f'(0) f'''(0) f''''(0) 8 0 10 0 72 Taylor series

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f(x) = sin

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Unformatted text preview: (x) + cos (x) 2 2 f'(x) = 2*sin(x)*cos(x)- 2 * cos(x) * sin(x) f(x) ~ f(0) + x*f'(0) + . .. ~ Taylor series Taylor series Taylor series: f(x) ~ f(c) + (x-c)*f'(c) + (x-c) *f''(c) +(x-c) *f'''(c) + . .. ~ 2 3 3! 2! Taylor series f(x) = ln x at x = 1 f'(x) = 1/x = x-1 f''(x) = -x-2 f'''(x) = 2x-3 f(1) = 0 f'(1) = 1 f''(1) = -1 f'''(1) = 2 Taylor series f(x) = ln x at x = 1 f(1) = 0 f'(1) = 1 f''(1) = -1 f'''(1) = 2 f(x) = 0 + (x-1)- (x-1) 2 + 2(x-1) 3 2 3! 2 f(x) = 0 Taylor series Taylor series: f(x+h) ~ f(x) + h*f'(x) + h *f''(x) + h *f'''(x) + . .. ~ 2 3 3! 2!...
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taylor - (x cos(x 2 2 f(x = 2*sin(x*cos(x 2 cos(x sin(x f(x...

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