Meeting 15 Introduction to Numerical Methods Error Analysis.

Slides:

Advertisements

Similar presentations

Part 1 Chapter 4 Roundoff and Truncation Errors PowerPoints organized by Dr. Michael R. Gustafson II, Duke University All images copyright © The McGraw-Hill.

Advertisements

3- 1 Chapter 3 Introduction to Numerical Methods Second-order polynomial equation: analytical solution (closed-form solution): For many types of problems,

Roundoff and truncation errors

Physics Tool Kit Units (S.I. System - Meters, Kg, S) Unit Conversion Scientific Notation Accuracy and Precision Significant Figures Dimensional Analysis.

Chapter 2 – Scientific Measurement

Approximations and Errors

Round-Off and Truncation Errors

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 3 Approximations and Errors.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 5 Approximations, Errors and The Taylor Series.

NUMERICAL ERROR ENGR 351 Numerical Methods for Engineers Southern Illinois University Carbondale College of Engineering Dr. L.R. Chevalier.

1 Error Analysis Part 1 The Basics. 2 Key Concepts Analytical vs. numerical Methods Representation of floating-point numbers Concept of significant digits.

Chapter 2: Scientific Measurement Ms. Campos

Significant Figures.  All measurements are inaccurate  Precision of measuring device  Human error  Faulty technique.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 31.

Introduction and Analysis of Error Pertemuan 1

Significant Figures/Significant Digits

Chapter 1.5 Uncertainty in Measurement. Exact Numbers Values that are known exactly Numbers obtained from counting The number 1 in conversions Exactly.

Section 2.3 Measurement Reliability. Accuracy Term used with uncertainties Measure of how closely individual measurements agree with the correct or true.

The Scientific Method 1. Using and Expressing Measurements Scientific notation is written as a number between 1 and 10 multiplied by 10 raised to a power.

Cup of coffee = ~ 200 ml Add drop of H 2 O = 0.05 mL New volume: ~200 mL or mL?? If you say you imply that the volume of the initial cup.

ENGR Introduction to Engineering1 ENGR 107 – Introduction to Engineering Estimation, Accuracy and Precision, and Significant Figures (Lecture #3)

ES 240: Scientific and Engineering Computation. Chapter 4 Chapter 4: Errors Uchechukwu Ofoegbu Temple University.

Let’s Talk Numbers Uncertainties of Measurements, Scientific Notation, and Significant Figures.

Unit 1- Units and Measurement Chemistry. Scientific Notation, Measurement, Accuracy, Precision, Error.

Scientific Measurements “measurement” could be defined as the process or the result of determining the magnitude of a quantity. Measurements can be made.

Honors Chemistry I. Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

ME 142 Engineering Computation I Computer Precision & Round-Off Error.

LECTURER PROF.Dr. DEMIR BAYKA AUTOMOTIVE ENGINEERING LABORATORY I.

Unit 1 Chapter 2. Common SI Units SI System is set-up so it is easy to move from one unit to another.

ACCURACY A description of how close measurement is to the true or accepted value of a measurement. Error or Absolute Error = Observed value – accepted.

Do Now: (3 minutes) 1. What are the definitions of precision and accuracy? 2. Why are precision and accuracy important when making measurements?

NUMERICAL ERROR Student Notes ENGR 351 Numerical Methods for Engineers Southern Illinois University Carbondale College of Engineering Dr. L.R. Chevalier.

MEASUREMENT. Chapter One: Measurement  1.1 Measurements  1.2 Time and Distance  1.3 Converting Measurements  1.4 Working with Measurements.

Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00.

Intro to Chemistry: Significant Figures!. There is uncertainty in all measurements. The “certain” digits include all numbers read directly off of the.

Significant Digits. l Significant figures are extremely important when reporting a numerical value. l The number of significant figures used indicates.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 3.

2.3 Using Scientific Measurements. Accuracy vs. Precision  Accuracy- closeness of measurement to correct or accepted value  Precision- closeness of.

Scientific Measurement Measurements and their Uncertainty Dr. Yager Chapter 3.1.

The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What.

Uncertainty and Significant Figures Cartoon courtesy of Lab-initio.com.

Errors in Numerical Methods

Significant Figures and Scientific Notation. What is a Significant Figure? There are 2 kinds of numbers:  Exact: the amount of money in your account.

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Using Scientific Measurements. Accuracy and Precision Accuracy –How close a measurement is to the true or accepted value Determined by calculating % Error.

ESO 208A/ESO 218 LECTURE 2 JULY 31, ERRORS MODELING OUTPUTS QUANTIFICATION TRUE VALUE APPROXIMATE VALUE.

Significant Digits or Significant Figures. WHY??? The number of significant figures in a measurement is equal to the number of digits that are known with.

Numerical Analysis CC413 Propagation of Errors. 2 In numerical methods, the calculations are not made with exact numbers. How do these inaccuracies propagate.

Chapter 2 © Houghton Mifflin Harcourt Publishing Company Scientific Method The scientific method is a logical approach to solving problems by observing.

Measurement: Significant Figures. Significant Figures  Significant Figures (sig. figs.): the number of digits that carry meaning contributing to the.

 Importance: to ensure the accuracy of our measurements  To make sure we tell others only what we actually know based on our equipment and it’s limitations.

 Importance: to ensure the accuracy of our measurements  To make sure we tell others only what we actually know based on our equipment and it’s limitations.

1 Approximations and Round-Off Errors Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Applied Numerical Method for Engineers Chapter.

Matter, Measurement, and Problem Solving. Measurement and Significant Figures Tro: Chemistry: A Molecular Approach, 2/e.

Chapter 2 Errors in Numerical Methods and Their Impacts.

Significant Figures.

ME 142 Engineering Computation I

Uncertainty in Measurement

SIGNIFICANT DIGITS INTRODUCTION

Chapter 2 ERROR ANALYSIS

Roundoff and Truncation Errors

Significant Figures Any digit in a measurement that is known with certainty plus one final digit, which is somewhat uncertain or estimated.

Significant Figures Aren’t all numbers important?!?!?!?

Mathematical Model.

Accuracy vs. Precision & Significant Figures

Roundoff and Truncation Errors

Accuracy vs. Precision Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured. Ex: if the correct.

SIGNIFICANT FIGURES.

SCIENTIFIC MEASUREMENT

Presentation transcript:

Meeting 15 Introduction to Numerical Methods Error Analysis

Numerical Methods Numerical methods are techniques by which mathematical problems are formulated so that they can be solved with arithmetic operations.

Why We should Study Numerical Methods 1. Numerical methods are extremely powerful problem-solving tools. 2. Numerical methods provide a vehicle to reinforce the understanding of mathematics.

Significant Digit The significant digits of a number are those that can be used with confidence. They correspond to the number of certain digits plus one estimated digit. Zeros are not always significant figures because they may be necessary just to locate a decimal point.

Significant Digit The numbers , , and all have four significant figures. When trailing zeros are used in large numbers, it is not clear how many, if any, of the zeros are significant.

Significant Digit

ACCURACY AND PRECISION Accuracy refers to how closely a computed or measured value agrees with the true value. Precision refers to how closely individual computed or measured values agree with each other.

(a)inaccurate and imprecise (b) accurate and imprecise (c) inaccurate and precise (d) accurate and precise.

ERROR DEFINITIONS Numerical errors arise from the use of approximations to represent exact mathematical operations and quantities. Truncation errors -> which result when approximations are used to represent exact mathematical procedures. Round-off errors -> which result when numbers having limited significant figures are used to represent exact numbers.

ERROR DEFINITIONS