Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Numerical methods
using taylor's series
Transcribed Image Text:Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from
780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five
wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of
change can be computed to eliminate unwanted signals.
Table 1
Wavelength, x (nm)
Measured Signal, E(x) (unit)
750
900
950
1000
1150
12.34
87.23
332.12
455.74
429.41
By applying all appropriate numerical first order derivative methods to the following questions:
(i)
Estimate the rate of change of the signal when the wavelength was 950 nm using an interval
of 50 nm.
(ii)
Estimate the rate of change of the signal when the wavelength was 950 nm using an interval
of 200 nm.
(iii)
Identify the best method in estimating the rate of change of the signals with a concise
justification if the exact solution is 2.4566.
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