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Phys 114 – Introduction to data reduction with Applications (3-0-3)
Spring 2010, Sect 002, 2:30-3:55 PM, M, 11:30-12:55 F, Room 101-T
| Topics : |
An introduction to both the theory and application of error analysis and data reduction methodology. Topics include the binomial distribution and its simplification to Gaussian and Poisson probability distribution functions, estimation of moments, and propagation of uncertainty. Forward modeling, including least-squares fitting of linear and polynomial functions, is discussed. The course enables students to apply the concepts of data reduction and error analysis using data analysis software applied to real data sets found in the physical sciences.
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| Objectives: |
By the end of the course, students should
- Be able to address the pros and cons of various methods of measurement
- Be conversant with the data reduction and error analysis concepts mentioned above,
- Be able to analyze 1D and 2D data sets to find computational estimates of PDFs, moments, and to address the appropriateness of various forward models,
- Be familiar with various measurement techniques so as to best experimentally determine PDFs, moments, and the appropriateness of various forward models,
- Be able to devise an experiment capable of making a measurement to a pre-determined level of precision,
- Be able to create figures that are journal-quality,
- Be extremely familiar with the Matlab software package so as to utilize it in subsequent classes and research endeavors.
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| Instructor: |
Dale E. Gary, Ph.D.
Email: dgary@njit.edu, Office: 101 TIER, Phone: 7878
Office Hours: MW 1:00-2:00 pm
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| Co-requisite: |
MATH 111
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| Course Materials: |
Bevington, P.R. and D. K. Robinson, Data reduction and error analysis for the physical sciences, 3rd ed. , McGraw-Hill, Boston, 2003.
Licensed use of MatLAB.
Syllabus PDF |
Course Requirements and Grading Policy :
Homework: 30%
Homework is given every week and is considered an important part of the class. The homework usually consists of reading the text, short answer questions, and numerous mathematical calculations. An assignment is given on the first lecture of the week [when theoretical material is covered] and will require measurements to be performed during that week either at the second lecture or outside of class. Students are encouraged to work together on the homework problems, though each student is responsible for handing in an individual homework set.
3 Exams (2 during the semester and 1 final, worth 20% each): 60%
The purpose of the exams is to test the individual student's progress in the class. Exams are closed book/notes. Exams will be announced ahead of time.
In-class quizzes and class participation 10%
There will be short, in-class quizzes at random times roughly every 2-3 weeks. In addition, attendance at lecture is expected and will be rewarded.
Grade Distribution: For each exam, and for the total of your homework grade, the grade distribution will be determined according to the gaussian (normal) distribution. This is called grading on a curve. It will also be determined on an absolute scale, as shown in the last column of the table below. We will discuss as a class which grading scheme is fairest, and why. If your final grade according to the Statistical Placement is worse than in the Absolute placement, then the latter will be used.
| Letter Grade |
Statistical Placement |
Absolute alternative placement |
| A |
>2 s above mean |
score > 85% |
| B |
>1 s above mean |
75% < score < 85% |
| C |
within 1 s of mean |
60% < score < 75% |
| D |
> 1 s below mean |
50% < score < 60% |
| F |
> 2 s below mean |
< 50% |
THE NJIT INTEGRITY CODE WILL BE STRICTLY ENFORCED AND ANY VIOLATIONS WILL BE BROUGHT TO THE IMMEDIATE ATTENTION OF THE DEAN OF STUDENTS.
Week |
Date |
Topic |
1 |
Jan 19 |
INTRODUCTION TO CLASS
MatLAB
Review of MatLAB: capabilities and programming environment
Forms of data (vectors, arrays, images as numbers)
APPLICATION: Write a basic MatLAB program
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2 |
Jan 25 |
More MatLAB
Making plots, using functions
Using HELP
APPLICATION: Write a basic MatLAB program to plot generated data (Homework "0")
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3 |
Feb 1 |
Methods of Measurement
(How to Make a Measurement, aka The Art of Measurements)
Basic matrix/array operations for reading in data and for graphical output
Choosing a plot scale, data vs. histograms
APPLICATION: Write a basic MatLAB program to read in real data and make a plot (Homework 1 HAT-P-6.xls, HAT-P-6.txt) |
4 |
Feb 8 |
Uncertainties in Measurement: Chap 1 Lecture 7 (ppt) Lecture 8 (ppt)
Parent distributions
Sample mean and sample standard deviation
Percent error, SNR—reduction of noise through repeated measurements
APPLICATION: Given a counting experiment [e.g., CCD] find various quantities Homework 2 |
5 |
Feb 15 |
Probability Distribution Functions: Chap 2 Lecture 9 (ppt) Lecture 10 (ppt)
Binomial
Gaussian, Poisson, Other [Lorentzian, Cauchy, etc.]
Moments, focusing on the first and second moments
APPLICATION: Determine the PDF for multiple random variables [temperature, CCD photon counts from previous week, sky brightness] Homework 3 |
X |
Feb 22 |
EXAM 1 (Review Feb 22, Exam Feb 26) Solution |
6 |
March 1 |
Error Analysis: Chap 3 Lecture 11 (ppt) Lecture 12 (ppt) Lecture 13 (ppt)
Statistical uncertainty
Bias
Propagation of Errors
Designing an experiment to make measurements to a particular precision
APPLICATION: Propagation of errors in a “complex” measurement: Measurements from a CCD Homework, Chap. 3 of the text, 3.1, 3.3, 3.5 Due Mar 8.
Chap. 3 of the text, 3.7, 3.11 Due Mar 22. |
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March 15 |
SPRING BREAK |
7 |
March 22 |
Estimators: Chap 4 Lecture 14 (ppt) Lecture 15 (ppt)
Chi-square, Student's t-Test
Moments: Mean, variance, skew, and kurtosis
APPLICATION: Spectral Kurtosis PDF Homework 5 |
8 |
March 29 |
The Forward Model I: Chap 6 Lecture 16 (ppt)
Linear and log-linear forward model and least-squares fitting to a linear data set
Homework Chap. 6 of the text, 6.4, 6.5 Due Apr. 5 |
X |
April 05 |
EXAM 2 (Review [ppt file] Apr 5, Exam Apr 9) Solution |
9 |
Apr 12 |
The Forward Model III: and Chap 7 & Chap 8 Lecture 17 (ppt) Lecture 18 (ppt)
Polynomial forward model and least-squares fitting to a polynomial data set
Generalized forward model
Generalized least-squares fitting
APPLICATION: Fitting a spectral line Homework 7 HW7_Prob1.xls HW7_Prob2.xls
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10 |
April 19 |
2D Data sets and fitting Lecture 19 (ppt) gaussfit2d.m MatLAB file for lecture 19
. Lecture 20 (ppt) Lecture20.m MatLAB file for lecture 20 fruit.gif (image file for use with Lecture20.m)
Creating 2D Gaussians and other functions
Convolution and deconvolution Homework 8
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11 |
April 26 |
In-Class Project
Project 1 (Monday and Friday) Project 1 Data ; |
12 |
May 3 |
Review for Final Exam (final will be on Friday, May 7) |
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