Course Description The first of two introductory-level laboratory courses. Introduces essential experimental techniques, including setup and operation of basic laboratory equipment, elementary experimental design, statistics and inference, and computational data analysis. Experimental techniques are introduced in the context of classic physics experiments. Instructor Professor David Pine E-Mail: pine@nyu.edu Telephone: 212-998-7744 Office: 601 Meyer Office hours: Mondays 4-6 p.m. (questions & homework help postmortem) Fridays 4-6 pm (questions & homework help premortem) and by appointment Lab Instructors Ellery Russell (for sections 002 & 003) E-Mail: ellery.russell@nyu.edu Office: 639A Meyer Chui-Lai Cheung (for sections 004 & 005) E-Mail: clcheung@nyu.edu
Office: TBD
Texts An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd Edition, by J. R. Taylor (University Science Books, Sausalito, 1997). [available at NYU Bookstore] Laboratory Notebook. [, click icon to view, available at NYU Bookstore] You need to buy this lab notebook, which make carbon copies of each page of your lab notebook. You must turn in those carbon copies at the end of each lab period. Python Manual, by D. J. Pine [downloadable, available under Resources link] Labs You will do 8 laboratory experiments. The first lab will take place the week of September 23rd. The table below shows the complete schedule of labs. While you will work with a partner, everyone turns in their own lab report, due one week after the lab. You are required to keep a lab notebook in this course. In it, you will document your activity during each experiment. Please note that you must show your lab notebook to your TA before you leave the lab each week so that it can be graded. See the handoutkeeping a Lab Notebook, available under Resources on NYUClasses, for tips on keeping a good lab notebook. There are no makeup labs. To make allowances for sickness, family emergencies, etc., the lab with the lowest score will be omitted in calculating your grade for this course. If you cannot attend a lab due to a religious holiday, you must notify the course instructor and your lab TA at least 2 weeks in advance in writing (e-mail is ok) so we can arrange for you to do the lab in one of the other lab sections for the course. There are four lab sections, which meet at the following times with Chui-Lai Cheung & Ellery Russell as TAs. Section 002, Mondays 12:30 pm - 3:30 pm, Ellery Russell Section 003, Tuesdays 2:00 pm - 5:00 pm, Ellery Russell
Section 004, Tuesdays, 9:15 am - 12:15 pm, Chui-Lai Cheung Section 005, Wednesdays, 9:00 am - 12:00 pm, Chui-Lai Cheung Date Experiment Room 23 September Motion 1&2 224 30 Septmeber Newton's 2nd Law 222 07 October Equilibrium of a Particle 221 21 October Conservation of Energy 222 28 October Work Energy 222 04 November Collisions in One Dimension 224 11 November Ballistic Pendulum 223 18 November Rotational Motion 222
Homework There will be weekly homework sets due on Mondays no later than 4:00 p.m. Copies of the problem sets as well as solutions will be posted on NYU Classes. Paper homework can be either (a) submitted in class on the due date or (b) be placed in a box in Meyer 424 (Physics Department office). Please note that there will be a different boxes depending on who your TA is: Chui-Lai (sections 004 [Wed 9-12] & 005 [Tue 9:15-12:15]) or Ellery (sections 002 [Mon 12:30-3:30] & 003 [Tue 2-5]). Computer homework should be uploaded on NYU Classes. Late homework will be accepted until the homework solutions are posted, which will be noon on the Wednesday two days after the Monday the homework is due. There is a 10% per day late penalty. Grading 60%: Lab notebooks and reports. Lab notebook, 0-15 points, Lab Reports, 0-85 points. You must turn in at least 6 competed labs with a score of 50 or better (out of 100) to receive a passing grade in this course. This means that you must receive at least (1) a score of 5/10 for your lab notebook (graded at the end of each lab AND (2) a total score of 50/100, including your lab report (due one week after each lab). Otherwise you will receive an F for the entire course. 20%: Homework 5%: Quizzes 15%: Final Exam [Monday, December 16, 10:00-11:50 a.m.] Lectures Lecture Meeting Times There is one lecture each week, with the following meeting place and time: Meyer 122
Mondays 11:00 a.m. - 12:15 p.m. September 9 Estimating uncertainty: Measuring Prof. Pine's height with a 2-meter ruler Estimating uncertainty in a measurement Random & systematic errors Significant figures Reporting uncertainty (absolute & fractional) in a measurement Discrepancy between measurements, graphical representation with error bars Graphing using error bars: estimating uncertainty of a slope Introduction to Python for science Canopy interface & code editor Interactive Python (IPython) shell IPython as a calculator Integers, floating point numbers, complex numbers Naming variables: always do it! Creating & running simple scripts Mathematical functions: NumPy library September 16 Propagation of uncertainties: Measuring Prof. Pine's height with a 50-centimeter ruler Uncertainties in a sum or difference add to give maximum uncertainty Uncertainties for products & quotients
Addition of relative errors Uncertainty in a counting experiment (preliminary treatment) Data Lists & Arrays Slicing arrays (and lists) Calculations with arrays Strings September 23 Quadrature addition rule & the random walk Independent uncertainties in a sum: positive and negative uncertainties partially offset each other Propagation of independent uncertainties for sums, differences, products, quotients Propagation of uncertainties for power laws Simple format specifiers Reading data from a data file Writing data to a data file September 30 Propagation of uncertainties: Deflection of laser beam by reflection Propagation of uncertainties for arbitrary functions of one variable Propagation of uncertainties for arbitrary functions of many variables General formula for propagation of uncertainties
Basic Plotting Plotting functions with continuous lines Plotting data with symbols October 7 Numerical differentiation and integration Numerical derivatives & subtraction: uncertainties increase Numerical integration & addition: uncertainties decrease Basic Plotting Plotting data with error bars Multiple plots in a single window October 14 - NYU University holiday October 21 Major Quiz October 28 Systematic, random errors, and repeated measurements Standard deviation; correspondence to estimated measurement error Standard deviation of the mean; improved measurement of experimental value Conditional statements: if, elif, & else Array conditional: np.where() function Loops: for & while Accumulators
List comprehensions November 4 User-defined functions Passing variables and arrays to functions: mutable and immutable objects Attributes and methods November 11 Least squares fitting of linear functions Chi-squared and goodness of fit. Role of uncertainty estimates (error bars) Visualizing chi-squared minimum as function of fitting parameters a, b,... Linear least squares: Coding with and without error estimates Plotting data with error bars and fit Plotting residuals November 18 Least squares fitting of linearized functions Transforming exponential and power-law functions to linear functions Determining error estimates of transformed data Coding exponential and power-law fits using linear least squares fitting Plotting using semi-log and log-log axes November 25
Least squares fitting of nonlinear functions Levenberg Marquardt algorithm: steepest gradient & quadratic approximation Visualizing chi-squared minimum as function of fitting parameters a, b,... Local & global minima in chi-squared Estimating good starting fitting parameters SciPy implementation of Levenberg Marquardt algorithm Examples of non-linear fits using SciPy LM algorithm December 2 Review: Propagation of errors Linear fitting of data Nonlinear fitting of data Plotting data and fits