05 - ENGR 201 Evaluation & Presentation of Experimental...

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4/26/2011 ENGR201 Lecture 5 Spring 2011 1 ENGR 201 Evaluation & Presentation of Experimental Data Lecture 5: Propagation of Error T. Chmielewski, Electrical & Computer Engineering D. Miller, Mechanical Engineering & Mechanics Drexel University 4/26/2011 ENGR201 Lecture 5 Spring 2011 2 Announcement - 1 • There will be no weekly quiz due to the midterm • Next week’s quiz will cover material from Lecture 4 and lecture 5 and accompanying problems and reading. • You will have 7 days from the time the midterm is scored to address any errors. After that the statute of limitations is exceeded and no action will be taken!
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4/26/2011 ENGR201 Lecture 5 Spring 2011 3 Announcement 2 On-line Midterm will be given this week - Week 5 Coverage reading and notes from lecture 1, 2, and 3 Homework problems for lectures 1, 2, and 3 Quizzes for lecture 1, 2, & 3 (including this week’s quiz) Test will be 90 Minute duration Test will be open from 12:01 (noon) Thursday thru 11:59 PM Friday containing multiple choice, true-false, vocabulary match and computational problems note problems will be weighted differently It is suggested that you have prepared a formula sheet and have a calculator or spread sheet program available There is NO MAKEUP 4/26/2011 ENGR201 Lecture 5 Spring 2011 4 Homework and Reading for Week 5 • Read text Chapter 5, Section 5.6 – skip paragraph on Monte Carlo analysis for now • Problems from textbook: 5.13, 5.14 • It is suggested you look up some additional material on Taylor Series and partial derivatives – see last slide for suggested websites
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4/26/2011 ENGR201 Lecture 5 Spring 2011 5 Propagation of Error – Uncertainties in your measured independent variable(s) “propagate” to uncertainties in the dependent variable – You can calculate the magnitude of the uncertainties in the dependent variable • Using derivatives if you know the mathematical relationship between the independent and dependent variables (such as a calibration curve) • Through a numerical approach that looks at the sum of the individual contributions of each uncertainty on the dependent variable 4/26/2011 ENGR201 Lecture 5 Spring 2011 6 Propagation of Error Case of 1 Independent Variable • Let y = f(x) define the relationship between dependent variable y and a measured independent variable x • We measure the independent variable, x a number of times, and establish its true value lies within the interval • Then there must also be an uncertainty in true value of y • We want a formal way to represent this relationship y ± δ y = fx ± tS x ( ) x tS x ±
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4/26/2011 ENGR201 Lecture 5 Spring 2011 7 Slight Diversion for Background Material Approximation of a function by Taylor Series •A power series is an infinite sum of the form: • A type of power series is the Taylor series. It represents a function f(x) as an infinite sum of terms defined about a single point, a .
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This note was uploaded on 05/18/2011 for the course ENGR 201 taught by Professor Miller during the Spring '08 term at Drexel.

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05 - ENGR 201 Evaluation & Presentation of Experimental...

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