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Comp 274 Week 2 Homework Assignment Pad

Physics 264L Syllabus, Fall 2015

Welcome       Time and Place       Prerequisites       What You Need       Class Policy       Weekly Reading       Grading

Exams       Labs       Homeworks       How to Write       Getting Help       Important Dates      


    Welcome to Physics 264L, Duke's physics course about modern physics, which mainly concerns two great advances of the 20th century, special relativity (the physics of the fast) and quantum mechanics (the physics of the small). The first third of the course will discuss Einstein's theory of special relativity (with some general relativity), while the remaining part of the course will provide an introduction to quantum mechanics. Numerous applications of relativity and quantum mechanics will be discussed throughout the semester, including applications to astronomy, biophysics, chemistry, condensed matter physics, nuclear physics, particle physics, and technology.

    Note: biophysics majors have the option of satisfying their modern physics and statistical physics requirements by taking the physical chemistry courses Chemistry 310 and 311 (and labs 310L and 311L), in place of Physics 264L and 363. If you have questions of which pair of courses is best for you, please talk with the Biophysics Director of Undergraduate Studies, Professor John Mercer.

Time and Place

    Classes will meet Mondays and Wednesdays from 10:05-11:20 AM in Physics 154.

    Students will also participate in one 2-hour lab each week that meets on Wednesday, Thursday, or Friday afternoons.


  1. The physics prerequisite is a full year of an introductory calculus-based physics course with labs, preferably the Physics 161-162 and 161L-162L sequences at Duke but also good are the Duke 141L-142L and 151L-152L intro physics sequences. AP Physics C (mechanics and "electricity and magnetism") is a weak physics background for 264L but is possibly ok provided that you have a sufficiently strong math background. (Please meet with Prof. Greenside before drop/add if you are not sure if you have a strong enough physics or math background for 264L.)
  2. The math prerequisite is multivariate calculus (corresponding to the Duke math courses 212 or 222), which you need to take before taking Physics 264L. The course will also use some linear algebra and elementary differential equations but this material will be introduced and explained during the semester, you do not need to know this material ahead of time.

What You Need:

  1. There are three required books:
    1. Special Relativity by A. P. French (W. W. Norton & Company, 1968)
    2. An Introduction to Quantum Physics by A. P. French and E. F. Taylor (W. W. Norton & Company, 1978).
    3. An Introduction to Error Analysis, Second Edition by John R. Taylor (University Science Books, 1996). This book is also used in the Advanced Physics Lab course, Physics 417S.

    We will cover about 60% of each of the first two books, skipping some chapters and skipping some material in the chapters that are discussed.

    You should also own a hard-copy calculus-based introductory physics textbook so that you can easily review the prerequisite physics during the semester. One good text is Physics for Scientists and Engineers: A Strategic Approach with Modern Physics, Third Edition by Randall Knight (Addison-Wesley, 2012) but any similar text is fine (by authors such as Young and Freedman, Tipler and Mosca, etc). These books also have good chapters on modern physics that will be useful for you to read during the semester.

    Also quite helpful for you to own is a book on mathematics for physics and engineering students such as Mathematical Methods in the Physical Sciences, 3e by Mary Boas (Wiley, 2005). Such a text provides an efficient way for you to review mathematics used in 264L and in other physics courses, including complex numbers, one-variable calculus, multivariate calculus, differential equations, linear algebra, and Fourier analysis.

  2. A computer with access to the Internet and a modern browser like Google Chrome or Mozilla Firefox. You will need to access email, the 264L webpage, the Duke Sakai website, the course Piazza website, and various websites and multimedia files as mentioned in class.
  3. The Mathematica computer mathematics program. As a Duke student, you can download and install a free copy of this software from the OIT site-licensed software webpage.

    Note: some of the homework assignments will include some Mathematica code for you to execute and think about, or will ask you to download, run, and think about pre-written Mathematica notebooks. Visualization and statistical analysis of your laboratory data can also be easily carried out using Mathematica, and Mathematica provides via its notebook interface a convenient way for you to typeset your homeworks and labs, including mathematical expressions, data tables, and plots. Beyond the Mathematica homework and lab examples, you are welcome to use any other computer language, e.g., Matlab if you are an engineering student.

Class Policy

    All students are expected to have read the Duke Community Standard and to comply with those standards throughout the semester.

    All students are expected to be respectful of each other and of the class and labs.

    Please arrive before the beginning of classes and of labs and be settled in so that each class and lab can start on time. Please do not start to leave the classroom until after the class has finished.

    Cellphones, laptops, and tablets are not to be used during lectures unless Professor Greenside gives you permission. These devices are highly distracting and substantially weaken the learning experience, not just for a student using one of these devices but for the other members of the class and for the teacher. You are allowed to use your laptops or tablets in the labs, but please stay focused on the lab.

    Weekly attendance in labs is mandatory. Since students will be working in groups and you cannot do these labs outside the 264L lab room, you need to come to lab each week for the full two hour period. If you are going to miss a lab because of illness or Duke-related travel, please contact Dr. Bomze as soon as possible before the lab you are going to miss. You will lose credit for labs that you miss without a valid excuse, and you will get an F for any lab for which you miss both of the related labs.

    No food is allowed in the labs. A drink is ok but only in a bottle that can be sealed with a cap (no open cups!), and these bottles must be kept away from computers and from the experimental equipment.

Weekly Reading

    The weekly reading will be posted on Piazza and will approximately follow the course schedule of topics and readings.

    It is extremely important that you complete the assigned reading before the first class of each week, and before the first lab of each week. There will simply not be enough time during class or during the labs to discuss all the details that you need to know, and you will get more out of the classes and out of the labs if you have already thought about the material.

    Please read the assigned material actively. This means you that, as you read a text or article, you should have a pen or pencil in hand with lots of blank paper, and that you should work through various derivations, take notes of key points, and keep a list of questions that you can ask in class or post on Piazza.


    Your final grade for the course will be based approximately on the following course components with the indicated weighting:

    Component   Percent of Total Grade   Final exam (3 hours) 35% Two in-class midterm exams (1.25 hours each) 30% Labs (5 total) 25% Homework assignments (approximately 10 total) 10%
    The reason for saying that your final grade will be approximately based on this table is that, before assigning a final grade, Professor Greenside will try to take into account additional information that might affect your grade such as discussions that Prof. Greenside or Dr. Bomze, or the TAs might have had with you over the semester that demonstrate good insight or extra effort, solutions handed in on extra credit homework problems, or illness or travel that might have prevented you from doing your best during the semester.

    These different course components are discussed in the following sections.


    The two midterm exams and final exam will be closed-book and no electronic devices of any kind will be allowed, including calculators. With a some exceptions (e.g., you are expected to know the values of key physical constants like c, , G, K, k, etc to the nearest power of ten in SI units), relevant equations and data will be provided with the exams so you can focus on demonstrating your conceptual and technical understanding of key topics.

    The first midterm will cover the material on relativity, the second midterm will cover material discussed after the first midterm, and the final exam will cover material over the entire semester, with an emphasis on material covered since the second midterm. Questions will be drawn from what was discussed in class, from the assigned reading, from the labs, and especially from the homework assignments.

    If you feel that a question on an exam was not graded correctly, you can request a regrade by your writing down on a page of paper your name, the date, the question that you would like regraded, and a brief explanation of why you are requesting a regrade. You should then give your regrade request and exam to Professor Greenside.

    It will not be possible to make-up a midterm exam. If you miss a midterm without a valid excuse, you will get a grade of F for that exam. If you know in advance that you will not be able to attend an exam (the dates are given below), please contact Professor Greenside as early as possible so that he can work out with you an alternative date for you to take the exam. If you miss a midterm because of some valid reason (illness, travel related to Duke etc), Professor Greenside will base your course grade on the other components of the course. If you miss the final exam, you will get a grade of X (incomplete) and have to take the final exam at some future date.


    Each student will do eight weeks of preparatory labs that involve learning how to record errors related to measurements, characterizing measurements by simple statistical quantities, learning how to use an oscilloscope, and becoming familiar with some optical equipment such as an optical bench, refraction and lenses, diffraction and interference of light, and the use of a Michelson interferometer. Then, in groups of two to three, students will complete at least three of the following seven labs:
    1. use a Michelson interferometer to measure the wavelength of visible light and the index of refraction of air;
    2. use a plastic scintillator and coincidence detector to measure the relativistic dilation of the muon lifetime.
    3. use a rotating mirror to measure the speed of light in air;
    4. study the photoelectric effect and use your results to estimate Planck's constant, the fundamental constant of quantum mechanics.
    5. use a two-slit interference device with a low- and high-intensity light source to study the wave-particle duality of photons.
    6. measure and study the universal blackbody radiation spectrum of a source in thermal equilibrium.
    7. study the wave property of electrons using diffraction of electrons from a piece of aluminum metal and from a piece of graphite.

    Each lab will take one to two weeks to complete. After completing a lab, you or your group will submit a printed (not handwritten!) lab report that will be evaluated by the Lab TA and then given a letter grade. Each member of a group will get the same grade for the lab report, but your final individual grade for a given lab will also depend on your active participation, as judged by Dr. Bomze or by the lab TA. Also someone who misses a lab without an approved excuse by Dr. Bomze will get a decreased grade for that lab.

    Lab reports are due no later than one week after the last lab session associated with a lab, and late lab reports are not accepted. The comments below in the Homework Assignments section regarding collaboration and cheating also hold for labs, so please make sure to read those.

    If your group feels that a lab report was not graded correctly, your group can request a regrade by your group writing down on a page of paper the names of the people in your group, the date, and a brief explanation of why you are requesting a regrade of your report. You should then give your regrade request and lab report to Dr. Bomze.

Homework Assignments

    There will be a homework assignment about once per week. You will hand in your assignment by putting it in the Physics 264L slot in the tall wood set of homework bins opposite the hall from Rm 141.
    Note that
    • Late homeworks are not accepted without an excuse that is approved by Professor Greenside before the homework's due date. Please be familiar with the information on the Duke webpage about Missing Work/Classes.
    • It is your responsibility to put your name and date on your assignment, to staple all pages together, and to hand your assignment in on time. The homework grader has Professor Greenside's permission to return to you ungraded any homeworks that lack a name, that are not stapled, or that are handed in late without a prior excuse approved by Professor Greenside.
    • You are not allowed to get homework answers from other students or from the Internet where complete solutions can often be found. This will be regarded as cheating which has serious consequences at Duke. In turn, you are not allowed to give complete answers to your classmates (including not posting solutions on Piazza). If a classmate asks for help, please give a suggestion or hint about what to try or do. You will learn much more if you struggle creatively to solve the problems on your own or by discussing them with your classmates or with the TA or with myself. Also keep in mind that 65% of your course grade will be based on the two midterms and final exam for which you will not have access to your textbooks, to the Internet, to a computer, or to your classmates.
    • You are allowed to collaborate with your classmates on an assignment, and Professor Greenside officially encourages collaboration. (This is realistic, scientists collaborate all the time in research.) However, you must write up your homework on your own, in your own words, and with your own understanding. Please also acknowledge explicitly in writing at the beginning of your assignment anyone who gave you substantial help, e.g. classmates or the course instructors. (Again, scientists usually acknowledge in their published articles colleagues that helped in completing some particular research.) Failure to write your homeworks in your own words (especially copying answers from a downloaded answer book) or failure to acknowledge help when given may lead to academic penalties so please play by the rules.

    Your lowest homework grade will be automatically dropped before determining your final homework grade for the semester. Either don't do one of the assignments or just let your lowest homework grade be automatically ignored. This also means that you don't have to ask permission or get an excuse to skip an assignment, e.g., if you are traveling out of town because of a Duke or family event.

    Assignments are intended to take from five to seven hours per week to complete, not including reading the text. If an assignment takes more than seven hours, something has gone wrong so please post a message on Piazza (anonymously if you like) that the assignment is too long. Professor Greenside can then email the class about how to reduce the duration of the assignment, e.g., by dropping parts of a problem or an entire problem.

    Since assignments can take up to seven hours to complete, please do not start an assignment the night before it is due, that will not give you enough time to think about the problems in a creative and productive way, nor give you time to get help if you need help. So please start working on each assignment a few days before the due date.

    Since it will not be practical for the grader to grade all the problems of all the students (that would be over 300 problems per week), the grader will grade a few problems from each assignment (you will not know ahead of time which problems will be graded). Although not all problems will be graded, you should strive to figure out how to solve all the problems so that you will be prepared for the midterms and for the final exam. Detailed answers will be posted for each assignment after its due date, and you should work through the solutions to make sure you have mastered the ideas and techniques.

    If you feel that one or more homework problems in a given assignment was not graded correctly, you can request a regrade. To do this, write down on a separate piece of paper your name, the date, and your email address, and then write down a concise explanation of which problem you feel was graded incorrectly and why. You should then give Professor Greenside your assignment and sheet, and he will meet with the homework TA to determine whether a regrade is appropriate and how many points should be restored if so.

How to Write Your Homeworks and Lab Reports

    When writing your homeworks and labs, please pay attention to details that improve the quality of your writing:
    • Write clearly. Writing clearly means using readable handwriting (no tiny or crowded script) and presenting your thoughts logically. You should strive to use proper grammar, correct spelling, and good sentence structure. For questions that require a symbolic answer, explain clearly how you obtained the answer, showing necessary steps with some brief phrases of explanation. Use plenty of space between symbols, and use blank lines to separate successive lines of equations. Keep in mind that paper is cheap compared to the time for you to solve and write up your answers, and compared to the time for the TA to read and grade your homeworks. You will get partial or no credit if the TA or the instructors can not easily understand your answers.
    • Write with insight. This means using complete sentences that explain and justify what you are doing. Especially in your homework solutions, brief answers like "yes", "no", or "ℏ/2" will not be given credit. Your written answers must be detailed enough to show us that that you understand how you got your answer and that you appreciate the significance of your answer. A simple criterion for a well-written answer is that you will be able to understand the answer yourself several weeks after you have written your answer, even without remembering what the original question was. Writing clearly especially pays off when it comes time for you to review your assignments and labs in preparation for the midterms and final exam. Writing clearly is also one of the most valuable skills you can develop at Duke.
    • All symbols should be given verbal names the first time you introduce them. For example, you should say "the wave function  Ψ" or "the angle θ in radians" instead of just writing the symbols Ψ and θ.
    • Physical units must be included with any numerical answer that corresponds to a physical quantity. For example, you should say "the distance was d=0.02 km", "the angle was a=5.3 rad", or "the magnetic field strength B had the value 2.3 T". In SI units, unit names like newton and tesla are not capitalized, while their abbreviated symbols like N and T are capitalized.
    • Graphs should be carefully drawn and their axes clearly labeled, and you should give the symbols and physical units of quantities associated with the horizontal and vertical axes. There should be a brief title or figure caption that describes what the graph is intended to illustrate, e.g., "Photocurrent I versus light wavelength λ", or "Comparison of Einstein's theoretical curve for the photocurrent I(λ) with experimental data".
    • Numbers obtained from a calculator or from a computer mathematics program like Mathematica should be rounded to the appropriate number of significant digits (see any introductory college physics textbook for a brief discussion regarding significant digits). For this course, two or fewer digits will suffice for most answers, and, in many cases, you will only be required to estimate some value to the nearest power of ten (no significant digits). Thus if you obtain on your calculator some result 7.38752103E-03, you should write this answer in your homework as 7×10-3 to one significant digit or as 10-2 to zero significant digits. You will lose points for giving too many significant digits in your homeworks, labs, and exams. Be especially careful not to report errors that have more digits than the quantity of interest, e.g., 3.8 ± 0.124 V would indicate you don't understand how to calculate errors (this should instead be written 3.8 ± 0.1 V).
    • For problems and labs (and especially for exam questions) that require obtaining the numerical value of some symbolic expression, you should first work symbolically to obtain a final concise simplified mathematical expression and only then substitute numerical values of parameters. In particular, avoid calculating intermediate numerical values that are not required as part of the answer. For example, consider calculating the rotational energy U = (1/2) I ω2 of some rigid rotating object whose moment of inertia about some axis is I = c1 M R2 and where the angular speed ω = v/R is known in terms of some speed v and radius R. Then to calculate the numerical value of the energy U, do not calculate the two unnecessary intermediate values I and ω. Instead, first combine all the expressions symbolically into one final reduced symbolic expression U = (1/2) c1 M v2 and then evaluate this expression numerically by substituting the values of the known parameters c1, M, and v. Note that simplifying the expression like this also clarifies the physics, here by showing that the answer does not depend on the value of the radius R.

Getting Help

  • Use Piazza    Questions about the course material, homeworks, and labs should be posted to the Physics 264L Piazza webpage. (Do not email such questions to Professor Greenside or to Dr. Bomze directly.) Piazza is an elegant web-based forum that allows members of a class, including instructors, to ask and answer questions. The main two benefits for you in using Piazza is that you can get rapid feedback (especially say in evenings and on weekends), and you will benefit when other members of the class ask questions and get answers via Piazza. Here some suggestions about using Piazza:
    • Do not be shy in asking questions about any part of the course. With Piazza, you can ask questions anonymously and please use this feature if this will make you feel more comfortable about asking a question. (It is much better for you to ask than to be frustrated). When someone submits an anonymous question on Piazza, not even the instructors know who asked the question.
    • You will get the most help on Piazza if you include details and ask something specific. Don't say something like "I am stuck with homework problem 3.1", say something like "Part (b) of problem 3.1 asks me to do the following, and I get to this particular point in the answer and then I am not sure what to do next." Or you could ask "How did the author derive Eq. (5-14) on page 137 of the French book?" or "In figure 3-6 on page 83 of the French book, why do the x' and ct' axes form the same angle with the x and ct axes respectively? Or you could ask "In the interferometer lab, I am not sure how to use the error propagation formula to estimate the error in the wavelength of light because of this particular detail."
    • You are not allowed to provide on Piazza or by email detailed solutions for homework problems or for experimental issues related to labs, such answers will be considered a violation of the Duke Community Standard. Instead, please provide hints or suggestions that allow a member of the class to make further progress on his or her own. If you are not sure whether your reply will provide too much information, email you reply to Professor Greenside or Dr. Bomze via a direct email to see what they think.
    • Please be polite and respectful in any reply you post. Physics is challenging, even for experienced physicists, and everyone struggles at some point to understand what is going on.
    • The only questions not appropriate for Piazza would be personal ones, such as questions about your scores and grades, or what to do if you will miss a class, lab, or exam because of illness or travel. For these questions, please contact Professor Greenside or Dr. Bomze directly.
  • Meet with an instructor    Professor Greenside is glad to meet with you if you have any questions about the course material, while Dr. Bomze is glad to meet with you regarding any lab-related questions.. To arrange a meeting, send an email or talk to an instructor in class. All the contact information is available at the top of this syllabus. Also, If somehow you fall behind or if you are finding the course more difficult than you had anticipated, please make an appointment to see Professor Greenside as soon as possible so he can find ways to help you.

Important Dates

    Aug  24, Mon      First class
    Sep  4, Fri      Drop/Add ends at 5 PM
    Sep  7, Mon      Class meets despite Labor Day
    Sep 30, Wed      First midterm exam
    Oct 12, Mon      No class, fall break
    Nov 4, Wed      Second midterm exam
    Nov 25, Wed      No class, Thanksgiving recess.
    Dec 2, Wed      Last 264L class.
    Dec 10, Thu      Final exam (2-5 pm)

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The first-line intervention for intermittent claudication is usually supervised exercise therapy (SET). The literature describes a range of exercise programs varying in setting, duration, and content. The purpose of the present study was to examine the exercise protocols offered and to identify the impact of the intensity of the SET programs (in terms of frequency, duration, and type of exercise) on improvements in walking distance (response) in the first 3 months. The present study is part of the Exercise Therapy in Peripheral Arterial Disease (EXITPAD) study, a multicenter randomized clinical trial comparing the effects of SET provided by regional physiotherapists, with or without daily feedback, on the level of activities with the effects of walking advice.


The analysis included patients randomized to receive SET with or without feedback. The physical therapists administering the SET were asked to fill out therapy evaluation sheets stating frequency, duration, and type of exercises. The relationship between training volume and the impact on walking distance was explored by dividing training volume data into tertiles and relating them to the median change in maximum walking distance at 3 and 12 months.


Data of 169 patients were included in the analysis. A SET program consisting of at least two training sessions per week each lasting over 30 minutes, during the first 3 months of a 1-year program tailored to individual patients' needs led to better results in terms of walking distance after 3 and 12 months than the other variants. The results of our analysis dividing training volume into tertiles suggest that there is a relationship between training volume and improvement in walking distance and that at least 590 minutes of training should be offered in the first 3 months. No differences were found between program involving only walking and a combination of exercises, nor between individual and group training.


A SET programs consisting of at least two training sessions a week, each lasting over 30 minutes, should be offered during the first 3 months of the SET program to optimize improvement in terms of maximum walking distance.