PHY6346: Electromagnetic Theory I

This course is the first semester of a two semester graduate level course on Classical electromagnetism. I will be assuming all in the class have mastered electricity and magnetism as taught at the advanced undergraduate level. We shall therefore take Maxwell's equations as a given, and concentrate on their applications to explaining a wide range of physical phenomena. A major goal of the course is to develop systematic mathematical methods for the solution of the equations in advanced contexts, and in a way that will be useful in all areas of theoretical physics. Our aim in the first semester is to cover most of the material in the first seven chapters of Jackson.

PHY6347: Electromagnetic Theory II

This course is the second semester of a two semester graduate level course on classical electromagnetism. We shall begin the semester with a discussion of Lorentz covariance and special relativity. (Chapters 11,12 of Jackson). We shall then return to Jackson's order of topics from plane waves through radiation by moving charges.

Below are links to course information, a syllabus, a convention and formula sheet. As the course develops, I will improve and update my lecture notes, which will be posted here.

Required text:

John David Jackson [@ucb] , Classical Electrodynamics, Third Edition (Wiley, 1999) [errata] [errata']

Course Information:

Class and contact Information

email: thorn@phys.ufl.edu

Lectures: MWF period 3 (9:35-10:25 am), NPB 1101

Discussion Class: F period (4:05-4:55), NPB 1216

Office hours: MW period 5 (11:45a-12:45p), NPB 2069 and by appointment

Our grader: Qiaoli Yang

email: qiaoliyang@phys.ufl.edu

Office hour: F period 8 (3:00-4:00pm) , NPB2038

Announcements, Spring 2012

Problem Set 1 posted 5 January 2012. Note that because of the Martin Luther King Holiday it will be due on Wednesday, rather than the usual Monday.
Problem Set 2 posted 13 January 2012.
Problem Set 3 posted 20 January 2012.
We have chosen the time and place for our extra discussion section each week. It will be every Friday, 9th period, 4:05-4:55pm in room NPB 1216. It is completely optional, and we will discuss anything that you wish to bring up, from confusing points in lecture to hints on homework problems.
Solution Set 1 posted 27 January 2012.
Problem Set 4 and updated lecture notes posted 28 January 2012.
Solution Set 2 posted 31 January 2012.
Problem Set 5 posted 3 February 2012.
I have tentatively chosen 2 March as the date for our midterm. I am willing to discuss alternatives to this date in the next couple of classes--Please make a special effort to attend classes next week, to make sure any change we decide on is compatible with all our schedules!
In class today (6 Feb), we discussed the midterm date, and all those present were agreeable to moving it from my tentative date, Friday 2 March, to Wednesday 29 February. I will wait a few days for objections from those not present in class today. If I hear none by Friday 10 February, the new midterm date will be adopted.
Solution Set 3 posted 6 February 2012.
Problem Set 6 posted 11 February 2012.
Solution Set 4 and Problem Set 7 posted 15 February 2012.
Solution Set 5 posted 20 February 2012
In accordance with popular demand, I am pushing the due date for Problem Set 7 back to 5pm Tuesday, 28 February. I will post Solution Set 7 immediately after that.
Problem Set 8 posted 24 February 2012.
The midterm examination to be given in class on 29 February will cover all material up to but not including waveguides. This material is covered in my lecture notes through section 9 and Problem Sets 1 through 7. The relevant chapters in Jackson are 11,12 and 7. There will be four problems, each valued at 25 points. As usual, the exam will be closed book, but the standard exam formula sheet will be appended to the exam booklet.
Solution Sets 6 and 7 posted 28 February 2012.
Problem Set 9 posted 1 March 2012.
Problem Set 10 posted 16 March 2012.
Problem Set 11 posted 24 March 2012.
Solution Sets 8 and 9 posted 26 March 2012.
Problem Set 12 posted 1 April 2012.
Solution Set 10 posted 2 April 2012.
Course and teacher evaluations are now being conducted entirely on line. They will start Thursday, 5 April and will continue until Wednesday, 25 April. These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the web site: https://evaluations.ufl.edu/evals/ where you can find instructions and links to a gatorlink login page. It is probably a good idea if you bookmark the page so you can easily find it in the future.
Problem Set 13 posted 6 April 2012.
Problem Set 14 and Solution Set 11 posted 11 April 2012.
Updated Lecture Notes, Parts I and 2, posted 15 April 2012.
Note that all late homework must be handed in to me by 5pm on the last day of classes, 25 April 2012.
Solution Set 12 posted 18 April 2012.
Solution Set 13 posted 20 April 2012.
Solution Set 14 posted 25 April 2012.
The final exams have been graded and are ready to be picked up. The statistics on the final are as follows: Average 65.9; Median 64; Range: 48-87.
The statistics on the total course score are: Average 73.19; Median 72; range 63-90. Above 75 A; 70-75 A-; Below 70 B+.

Homework Assignments, Second Semester

In the homework assignments, I will refer to problems in Jackson's book by prefixing the problem number with J.

Problem Set 1, due 18 January 2012, Solution Set 1
Problem Set 2, due 23 January 2012, Solution Set 2
Problem Set 3, due 30 January 2012, Solution Set 3
Problem Set 4, due 6 February 2012, Solution Set 4
Problem Set 5, due 13 February 2012, Solution Set 5
Problem Set 6, due 20 February 2012, Solution Set 6
Problem Set 7, due 28 February 2012, Solution Set 7
Problem Set 8, due 12 March 2012, Solution Set 8
Problem Set 9, due 19 March 2012, Solution Set 9
Problem Set 10, due 26 March 2012, Solution Set 10
Problem Set 11, due 2 April 2012, Solution Set 11
Problem Set 12, due 9 April 2012, Solution Set 12
Problem Set 13, due 16 April 2012, Solution Set 13
Problem Set 14, due 23 April 2012, Solution Set 14

Information on Examinations

The final exam is scheduled for 3 May 2012, 7:30-9:30am. The midterm date is now fixed: It will be given in class on Wednesday, 29 February 2012. In grading the midterm and final exams, points will be deducted for errors in calculation and logic. Both exams will be closed book.

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

- T. S. Eliot

Announcements, Fall 2011

Generally I would like the homework to be handed in at the beginning of class on the due date. However, I will accept without penalty homework handed to me in my office (not in my mailbox!) before 5pm on the due date.

Problem Set 2 posted 26 August 2011.

Our course has been assigned a grader, Lili Deng, whose email, office and office hours are listed above. Please go to him first if you have any issues with the way your problem solutions are graded.

I will do my best to post solutions to the problem sets after 1 week past the due date as possible. Please remember that if an assigned problem is causing difficulty, I will be happy to help during my office hours.

Grading guidelines: Each problem handed in by the due date can earn a maximum of 10 points. Of these 6 points will be assigned by the grader based on the correctness of the solution. An informative title will earn 1 point. The remaining 3 points will be assigned by me on the basis of the clarity and style of your presentation. The maximum score on late homework will be 8 points if less thatn 1 week late and 5 points if more than 1 week late.

Problem Set 3 posted 2 September 2011.

Solution Set 1 posted 5 September 2011.

Problem Set 4 posted 10 September 2011.

Please note that problem 13 of Set 4 has been revised, reducing the number of required calculations, 12 September 2011.

Tomorrow (14 September) we will discuss setting a date for the midterm. The midterm will cover the material presented in class through 12 October and Problem Sets 1-7. I will post Problem Set 8 by 10 October, but it will not be due until 24 October, after the midterm. The possible dates for the midterm will be 14, 19, 21 October. (17 October is the classical mechanics midterm).

In class we chose 21 October for the date of our midterm. See the previous announcement for details on the material to be covered. The exam will be given during class period on this date.

Problem Set 5 posted 17 September 2011.

Solution Set 2 posted 18 September 2011.

Solution Set 3 posted 19 September 2011.

Problem Set 6 posted 23 September 2011.

Solution Set 4 posted 26 September 2011.

Problem Set 7 posted 1 October 2011. Please note that this will be the last homework set covered by the midterm exam on 21 October2011.

Solution Set 5 posted 3 October 2011.

Solution Set 6 posted 11 October 2011.

Problem Set 8 posted 13 October 2011. Note that this assignment is due 24 October 2011. In view of the midterm next week, there is no homework due on 17 Ocober.

Solution Set 7 posted 17 October 2011.

Problem Set 9 posted 21 October 2011.

Problem Set 10 posted 30 October 2011.

Solution Set 8 posted 31 October 2011.

Problem Set 11 posted 4 November 2011.

Solution Set 9 posted 9 November 2011.

Problem Set 12 posted 11 November 2011.

Course and teacher evaluations are now being conducted entirely on line. They start today (16 November) and will continue until 7 December. These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the web site: https://evaluations.ufl.edu where you can find instructions and links to a gatorlink login page. It is probably a good idea if you bookmark the page so you can easily find it in the future.

Solution Set 10 posted 16 November 2011.

Problem Set 13 posted 18 November 2011.

Solution Set 11 posted 22 November 2011.

PLEASE NOTE: To receive partial credit, all late homework must be handed in to me by 5pm on 7 December 2011, the last day of class.

Problem Set 14 posted 26 November 2011. This is the last assigned homework.

Solution Set 12 posted 28 November 2011.

Solution Set 13 posted 5 December 2011.

Solution Set 14 posted 7 December 2011.

Homework Assignments, First Semester

In the homework assignments, I will refer to problems in Jackson's book by prefixing the problem number with J.

Problem Set 1, due 29 August 2011, Solution Set 1
Problem Set 2, due 7 September 2011, Solution Set 2
Problem Set 3, due 12 September 2011, Solution Set 3
Problem Set 4, due 19 September 2011, Solution Set 4
Problem Set 5, due 26 September 2011, Solution Set 5
Problem Set 6, due 3 October 2011, Solution Set 6
Problem Set 7, due 10 October 2011, Solution Set 7
Problem Set 8, due 24 October 2011, Solution Set 8
Problem Set 9, due 31 October 2011, Solution Set 9
Problem Set 10, due 7 November 2011, Solution Set 10
Problem Set 11, due 14 November 2011, Solution Set 11
Problem Set 12, due 21 November 2011, Solution Set 12
Problem Set 13, due 28 November 2011, Solution Set 13
Problem Set 14, due 5 December 2011, Solution Set 14

Information on Examinations

The final exam is scheduled for 15 December 2011, 12:30-2:30pm. The midterm will be given, in class, on 21 October 2011. In grading the midterm and final exams, points will be deducted for errors in calculation and logic. Both exams will be closed book.

Announcements, Spring 2011

Lecture Notes updated through Section 8.3, 5 January 2011.
Statistics on last semester. Midterm average: 60. Final Exam average: 81/100. Homework average: 85/100. Total score average 75/100. 84-100 A; 73-83 A-; 63-72 B+; 59-62 B.
Problem Set 1 posted 7 January 2011.
Problem Set 2 posted 12 January 2011.
Problem Set 3 posted 21 January 2011.
Problem Set 4 posted 28 January 2011.
Solution Set 1 posted 28 January 2011.
Lecture Notes updated through Section 8.7, 23 January 2011. Some typos corrected and updates through Section 8.8, 30 January 2011
Solution Set 2 posted 1 February 2011.
Problem Set 5 posted 4 February 2011.
Lecture Notes updated through Section 8.9, 7 February 2011, some typos corrected.
Solution Set 3 posted 7 February 2011.
Problem Set 6 posted 12 February 2011.
Solution Set 4 posted 15 February 2011.
Today (16 February) the class discussed possible dates for the midterm and tentatively agreed on 4 March (the day before spring break) as the most desirable date. If you were absent from this discussion and have a conflict with this date, please let me know ASAP so we can discuss alternatives (2 March or 14 March) in class on Friday (18 February)!
Problem Set 7 posted 18 February 2011. I received no objections to the tentative date for the midterm, so the date, 4 March 2011, is no longer tentative.
Solution Set 5 and Solution Set 6 posted 28 February 2011.
In Problem 25 a) of set 6, the quoted form of the answer had a sign and factor of two error, which has been corrected. the factor (1+i(delta)^2/alpha) should read (1-i(delta)^2/2alpha).
Last year's midterm and exam formula sheet are posted here.
Solution Set 7 posted 2 March 2011. Solution to problem 28 (J. 7.24) completed 4 March 2011.
Lecture notes updated through Section 10.2, 2 March 2011.
Midterm results: Range: 39--95, Average: 76, Median: 78.
Problem Set 8 posted 7 March 2011.
Problem Set 9 posted 20 March 2011.
Lecture Notes updated through Section 11.1, 25 March 2011.
Problem Set 10 posted 25 March 2011.
Solution Set 8 posted 28 March 2011.
Problem Set 11 posted 3 April 2011.
Solution Set 9 posted 6 April 2011.
Problem Set 12 posted 8 April 2011. This is the last assigned problem set, due on 18 April 2011. Please remember that all late homework must be turned in to me by 5 pm on the last day of classes 20 April 2011. I will post all remaining solution sets at that time.
Lecture Notes updated through Section 12.1, 8 April 2011.
Lecture Notes updated through Section 12.3, 10 April 2011.
I am pushing back the due date for Problem Set 12 to the last day of classes 20 April 2011.
Solution Set 10 posted 11 April 2011.
Lecture Notes updated through Section 12.5, 13 April 2011.
Lecture Notes updated through Section 12.7, 18 April 2011.
Solution Set 11 posted 18 April 2011.
Solution Set 12 posted 22 April 2011.
Last year's final and exam formula sheet are posted here.
Problem Set 12 has been graded--you may pick it up any time at my office.

Homework Assignments, Second Semester

In the homework assignments, I will refer to problems in Jackson's book by prefixing the problem number with J.

Problem Set 1, due 19 January 2011, Solution Set 1
Problem Set 2, due 24 January 2011, Solution Set 2
Problem Set 3, due 31 January 2011, Solution Set 3
Problem Set 4, due 7 February 2011, Solution Set 4
Problem Set 5, due 14 February 2011, Solution Set 5
Problem Set 6, due 21 February 2011, Solution Set 6
Problem Set 7, due 28 February 2011, Solution Set 7
Problem Set 8, due 21 March 2011, Solution Set 8
Problem Set 9, due 28 March 2011, Solution Set 9
Problem Set 10, due 4 April 2011, Solution Set 10
Problem Set 11, due 11 April 2011, Solution Set 11
Problem Set 12, due 20 April 2011, Solution Set 12

Information on Examinations

The final exam is scheduled for 27 April 2011, 12:30-2:30pm. The midterm will be given on 4 March 2011, in class. In grading the midterm and final exams, points will be deducted for errors in calculation and logic. Both exams will be closed book.

Announcements, Fall 2010

Chapters 1-2 of lecture notes updated 8/24/10; some error corrections on 1-2: 8/26/10.
Problem Set 2 posted: 8/26/10.
Chapter 3 through 3.2 of lecture notes updated 9/4/10.
Problem Set 3 posted 9/4/10.
Solution Set 1 posted 9/7/10.
Problem Set 4 posted 9/10/10.
Sections 3.3 through 3.5 of lecture notes updated 9/11/10.
Clarification on late homework policy: If you hand in only some of the problems of a given set on time, those problems are eligible for full credit. In other words the late penalties only apply to the specific problems that are handed in late.
Solution Set 2 posted 9/13/10.
Problem Set 5 posted 9/17/10.
There is an error in the second equality of the second equation listed in problem 14 (Set 4). It has now (9/19/10, 2:45p) been corrected, thanks to Mr. Rinkevicius.
Sections 3.6 through 3.8 of lecture notes updated 9/20/10.
Solution Set 3 posted 9/21/10.
Problem Set 6 posted; Sections 3.9 and 3.10 of lecture notes updated 9/24/10.
Solution Set 4 posted 9/27/10.
After discussion in today's class we have agreed to have the midterm on Monday, 25 October 2010.
Problem Set 7 posted, 3 October 2010.
Lecture notes updated through section 4.2, 10/6/10.
Solution Set 5 posted 10/6/10.
Problem Set 8 posted, 8 October 2010. Note that the midterm exam to be given on 25 October will cover sets 1 through 8.
Solution Set 6 posted 10/11/10.
At the request of many who are studying for other exams, I have moved back the due date for Set 8 to Wednesday 20 October 2010.
Lecture Notes updated through Chapter 4, 13 October 2010.
Solution Set 7 posted 10/18/10.
Solution Set 8 posted 10/21/10. This solution set is posted early this week in view of the upcoming midterm. The midterm will cover lectures through yesterday (20 October 2010), problem Sets 1 through 8, and chapters 1 through 4 of Jackson. The exam booklet will include a two page formula sheet, which you can peruse here.
Problem Set 9 posted, 22 October 2010.
Problem Set 10 posted, 31 October 2010.
Lecture Notes updated through Section 5.5, 1 November 2010.
Problem Set 11 posted, 7 November 2010.
Solution Set 9 posted, 8 November 2010.
Problem Set 12 posted, 14 November 2010.
Solution Set 10 posted, 16 November 2010.
Lecture Notes updated through Section 6.3, 16 November 2010.
Problem Set 13 posted, 19 November 2010.
All late homework must be turned in to me by 5pm on the last day of classes (8 December 2010). I will post my solutions to any remaining assigned problem sets at that time. The last homework will be Set 14 to be posted in a week or so, and due on 6 December 2010.
Solution Set 11 posted, 23 November 2010.
Lecture Notes updated through Section 6.5, 24 November 2010.
Problem Set 14 posted, 24 November 2010.
Note that I have shortened the work you need to do for the last problem of Set 14 (J, problem 7.3): only answer the questions 7.3 a) and b) for the case of polarization perpendicular to the plane of incidence. 28 November 2010.
Solution Set 12 posted 29 November 2010. Note also that the due date for the final problem set 14 has been pushed back two days to the last day of classes, 8 December 2010.
Lecture notes, part I has now been completely updated 5 December 2010. The final examination will cover the whole course, Lecture notes through section 7.4 and all 14 problem sets. If you are interested, I have posted last year's final exam here for your perusal. Solutions to Sets 13 and 14 will be posted after the deadline for all late homework, 5 pm, 8 December 2010.
Solution Sets 13 and 14 posted 8 December 2010.

Announcements Fall 2009

For students interested in high energy physics: there is a high energy theory students group journal club every Tuesday at 4:30 in NPB 2165.
Lecture notes updated 9/3/09, sign errors in Eq 42,43 fixed.
Problem set 3 posted, 9/7/09, Solution Set 1 posted, 9/8/09
Problem set 4 posted, lecture notes updated, 9/14/09,
Solution set 2 posted, 9/15/09, error in 4d) corrected 9/16/09
Problem set 5 posted, 9/21/09, Solution Set 3 posted 9/22/09
Lecture notes updated, 9/24/09, 9/25/09
Because the last two problems (18 and 19) of Set 5 depend on material not yet covered in class, they will be incorporated in Set 6 and won't be due until Set 6 is due.
Problem set 6 posted, 9/27/09
In class on Monday, 9/28/09, we will discuss the date of our midterm. It will be an in-class closed book exam on a day free of exams in classical and quantum mechanics.
After class discussion, we have selected Monday 26 October for our midterm exam. There will be a normal homework asignment due on 19 October, but none due on 26 October.
Solution Set 4 posted, 9/29/09
Lecture notes updated, 10/2/09. Note that the recursion relations for ordinary Bessel functions (J,N,H) eq(133) need to be modified for the I,K Bessel functions eq(134). (In the older notes, no distinction was made for the different cases.) Also, some typos have been found and corrected.
Problem Set 7 posted, 10/4/09, Solution Set 5 posted 10/6/09
Please note that the notation in the first problem of set 7 was inadvertently reversed compared to the class discussion (the roles of z and w have been switched!).
Problem Set 8 posted 12 October 2009. There will be no homework assigned next Monday due to the midterm scheduled for Monday 26 October.
Solution Set 6 posted and lecture notes updated, 10/14/09
The midterm exam will be given Monday 26 October 2009 during the regular class period. Material covered will be Jackson Chapters 1-4, lectures through Monday 19 October 2009, and Problem Sets 1-8. There will be no problems on the midterm involving Bessel functions. A sheet of useful formulae will be printed on the exam and you may peruse it here.
Solution Set 7 posted, 10/20/09
Problem Set 9 posted and lecture notes updated, 22 October 2009.
Solution Set 8 posted, 10/28/09
Problem Set 10 posted, 1 November 2009.
Lecture notes updated, 4 November 2009.
Please note that I have added commentary on problem 33 (J,5.18) of Problem Set 10, which reduces the amount of work required for full credit.
Problem Set 11 posted, 8 November 2009.
By popular request the last two problems of Problem Set 10 are hereby moved to Problem Set 11. Only the first two are due today. Problem Set 11 now has 5 problems and is still due next Monday (16 November 2009).
Solution Set 9 posted, 10 November 2009.
Please note that I have revised the hints for problem 34 (Jackson 5.23), which is now the first problem of set 11: It is much easier to get the force, which the image cylinder exerts on the original one, by regarding each magnetized cylinder as a stack of current loops instead of as a pair of oppositely charged disks. Unfortunately, my original suggestion leads to much nastier integrals! My apologies.
Lecture notes updated, 13 November 2009.
For help with the mathematical aspects of this course I recommend the book Mathematics for Physicists by Dennery and Krzywicki. For properies of spencial functions I find Abramowitz and Stegun very useful, and for tables of integrals, Gradshteyn and Ryzhik. All of these books are listed in Jackson's bibliography, pp785-790.
Problem Set 12 posted, 16 November 2009.
Solution Set 10 posted, 19 November 2009. There will be a mathematical methods help session following our class on Friday 20 November.
Problem Set 13 posted and lecture notes updated, 21 November 2009.
Solution Set 11 posted, 25 November 2009.
Problem Set 14 posted, 30 November 2009. This is a very light problem set (only two problems). The last day of classes (9 December) is the last day late homework will be accepted. Remember that homework more than one week late can still be handed in by that date for half credit.
Solution Set 12 posted, 1 December 2009.
Lecture notes updated and Solution Set 13 posted , 7 December 2009.
Solution Set 14 posted and exam formula sheet updated, 11 December 2009.

Announcements, Spring 2010

For students interested in high energy physics: there is a high energy theory students group journal club every Tuesday at 4:30 in NPB 2165.
Problem Set 1 posted 10 January 2010.
Lecture notes updated, including some error correction 13 January 2010.
Problem Set 2 posted 17 January 2010.
Lecture notes updated 20 January 2010.
We will have a special math methods section on Fridays 5th period (11:45-12:35) in NPB 1200.
There was a typo in the first displayed equation of Set 2 problem 7: I_2 involves the dot product of E with B NOT the cross product. This is now corrected.
Problem Set 3 posted 23 January 2010.
Solution Set 1 posted 26 January 2010.
Problem Set 4 posted 31 January 2010.
Lecture notes updated 31 January 2010.
Solution Set 2 posted 1 February 2010.
Problem Set 5 posted 7 February 2010.
Solution Set 3 posted 8 February 2010.
Problem Set 6 posted 14 February 2010.
Solution Set 4 posted 15 February 2010.
After discussion our class chose Wednesday 3 March for our midterm. The exam will be in class.
Lecture notes updated 17 February 2010.
Problem Set 7 posted 21 February 2010. Shortened Set 7 posted 22 February 2010.
Solution Set 5 posted 22 February 2010.
Problem Set 8 posted 28 February 2010.
Solution Set 6 posted 1 March 2010.
Solution Set 7 posted 2 March 2010.
Lecture notes updated 10 March 2010.
Problem Set 9 posted 11 March 2010.
Problem Set 10 posted 21 March 2010.
Lecture notes updated 23 March 2010.
Problem 37 (J, 9.6) of Set 10 will be moved to the next Set 11, which will be due on 5 April. This reduces the assignment due on 29 March to three problems, one on excitation of waveguides and two on radiation from charges in uniform circular motion.
Problem Set 11 posted 28 March 2010.
Solution Set 8 posted 28 March 2010.
Solution Set 9 posted 30 March 2010.
Problem Set 12 posted 4 April 2010.
Solution Set 10 posted 5 April 2010.
Lecture notes updated 5 April 2010.
Problem Set 13 posted 11 April 2010. The last day of classes (21 April 2010) is the last day late homework will be accepted. Remember that homework more than one week late can still be handed in by that date for half credit.
Lecture notes updated 13 April 2010.
Solution Set 11 posted 13 April 2010.
Lecture notes updated 15 April 2010.
Lecture notes updated 20 April 2010: Table of Contents added.
Exam formula sheet updated 21 April 2010. Exam formula sheet.
Solution Set 13 posted 22 April 2010. Solutions for all problem sets are now posted.
The final examination had a median score of 68 and an average of 68.4. The range of scores was 51-88. The class total score (exams +HW) ranged from 61.72 to 88.18 with an average of 73.4. Total scores above average received an A- or A. Those below received a B+ or B.