Unofficial Advice
on math needed for
"physics with calculus"

from Dr. James Carr
Office: SM 290
Phone: 201-8971


Office hours   can be found here   along with E-mail addresses

Last Updated: 30 July 2009

Success in physics depends on your ability to do three things:

(1) Learn the basic principles and equations of "classical mechanics", including Newton's Laws and conservation of momentum and energy, and when to apply them;

(2) Read word problems, figure out what principle must be applied (identify the problem), and set up the appropriate equations;

(3) Apply basic mathematics skills (algebra and trig) to simplify and solve systems of equations and use mathematics as the language in which new ideas are expressed.

Of these three, weaknesses in math preparation (items 3 and 2) appear to be the main reason students struggle in this class, although some never do enough homework to become proficient in the application of physics to those problems.

First, a "C" is not enough in the pre-calculus math classes if you plan to take calculus and physics together. Years of experience say that students who did not do well in easy classes like trig or pre-calc (ones who earned only a "C", particularly if they had to repeat the class) are likely to fail physics and/or calc I on their first attempt. If you don't believe me, look at the data towards the bottom of this page. Better yet, read what your fellow students say about what trig you need to know to pass physics and calculus and ask yourself if you still know all of those things. My graduates in engineering school will also tell you that you need to remember all of that stuff, and big parts of what is in PHY2048, next year as well as next month.

I want to emphasize the importance of doing well in physics (or calculus) on your first attempt. Even if you find yourself struggling, quitting early means you have only learned maybe half of a third of the course. (It is not easy to build on 17% understanding when you repeat the class.) Further, a "C" is not enough in calc I if you plan to become an engineer. Engineers should definitely check out a separate advising page for engineers as well as the PDF file of my Advising Info for Engineering Majors and pay particular attention to the strict failure-repeat rule of the FAMU-FSU College of Engineering.

Second, although PHY2048 is a calculus-based physics course, calculus takes a secondary role to algebra, trig, geometry, and thinking. We make extensive use of vectors (a topic I quickly review because it is rarely covered thoroughly in trig classes) and solve problems that can involve geometry, trig, and doing algebra with several equations in several unknowns. Those math topics are not reviewed, but you will see them applied in examples. Calculus is introduced slowly so students taking Calc I will have seen the methods in a math class before we use them in the physics class, but you will be expected to use calculus on the final exam.

Third, PHY2048 is a very challenging course that should not be taken simply because PHY1053 is not being taught or is full. PHY2048 is much harder than PHY1053. Students who are only required to take PHY1053, such as pharmacy or architecture majors planning to go to FAMU, should not take PHY2048 even if it is not possible to take PHY1053 during the current semester. They should wait, and take PHY1053 in the fall, or get permission to take it as a transient student at one of the two universities in town.

 

Some Key Recommendations

(A) Students in the AS engineering program should complete Calc I before enrolling in PHY2048 unless they got an A in both trig and precalc. Take classes that apply trigonometry (such as surveying) along with calculus, and finish Calc II before taking physics if don't get an A or very high B in Calc I.

(B) No one should take MAC2311 and PHY2048 at the same time if they earned a C in either MAC2140 (pre-calc), MAC2114 (trig), or MAC2137 (combined trig and pre-calc) or had to repeat those classes. Very few students with those grades manage to succeed in physics. If you have a C in one of these classes, I strongly advise you to either

1. pass Calc I (MAC2311) before taking physics, or
    
2. "audit" the class you did poorly in and improve your skills, then take both MAC2311 and PHY2048 if you got over 87% while auditing that class.

(C) Workload:
There is strong evidence for a "workload" problem. Think of it this way: taking both PHY2048 and MAC2312 is harder than taking MAC1105, trig, and pre-calc at the same time, not even counting time for lab reports. Students who have not taken an actual freshman college level course (such as CHM1045 or MAC2311), let alone two of them at the same time, are often surprised at the amount of studying required. If you don't remember what you learned in previous classes, it is even worse. There is little review in college-level classes, unlike what you may have come to expect from the high-school level math classes you have been taking. Even students who have passed MAC2311 are sometimes surprised by the workload in MAC2312 and must drop physics to be able to pass calculus, although that is less common now that we use the "early transcendental" approach that makes MAC2312 only a bit harder than MAC2311 for students who still know all of calculus and trig.

(D) I do not recommend taking a break between MAC2311 and 2312 because Calc II is probably the hardest course of the seven that engineers must pass. You don't want to forget anything from MAC2311 before taking MAC2312. If your workload does not leave enough time for the 20 to 25 hours per week needed to study for both MAC2312 and PHY2048, you should take MAC2312 first. [One good time to do this is in the summer, but don't take anything else at the same time as Calc II in the summer.] There is less of a problem if you take a break between MAC2312 and your other calculus classes. Besides, you can stay in practice by helping your friends who are taking calculus!

 

The Data - Success Rates

My recommendations are based on hard data, not guessing. I'll discuss the results here. The methodology is at the bottom of this page for those who might be interested.

There were two studies done, one in the 2003-04 school year (when TCC used the "late transcendental" curriculum), and one in the 2008-09 school year (with the "early transcendental" curriculum that puts a greater premium on knowing the properties of the trig and log functions in Calc I).

(The passing rate for students who place directly into calculus from high school would be over 85% if I include only those who did so in this century.)

The 2003-04 data also indicated that everyone who passed physics also passed MAC2311, whereas only about 15% of the students who dropped physics managed to pass MAC2311. This is further evidence that most of the failing students do not remember (or never knew) enough math, rather than lack the time to study for both classes. They struggled even after cutting their class load in half. It also supports the common observation that MAC2311 was easier than PHY2048 or MAC2312 at that time.

The 2008-09 data included several instances of students who passed physics while failing MAC2311 or after getting permission to withdraw from MAC2311. All of these were in the "C or repeat" category. There were few instances of students dropping MAC2312 to concentrate on PHY2048. Together this suggests that these three classes might now be of comparable difficulty, which makes MAC2311 much more of a shock for a student who struggled in an easy class like trig.

But that is a relatively minor change. Even if we exclude the cases where a student failed to pass Calc I, the entry in the first box only changes from 40% to 29%. It is evident that students who pass trig and pre-calc today are much better prepared for the rigors of calculus and physics. My thanks (and yours, I trust) to my math colleagues for this improvement. Many more have gotten the message that they will need to remember this material, and improved success has been the result.

(I hope that the info from that first study, and the advice some former students gave about trig played some role in getting the message out to our students. I know that many continue to excel at FSU because they learned the importance of learning rather than simply passing a class.)

The slightly higher pass rate in physics for students who pass calculus despite a C in a pre-calc or trig class shows that some of these students correct their algebra deficiencies while taking calculus, but maybe half do not. Notice, however, that reasonably well-prepared students (A and B grades in trig and pre-calc) have a success rate that is almost the same whether or not they have passed calculus before taking physics.

The Data - Grades

I also looked at one other measure of success, which was the withdrawal rate and the GPA of each group of students.

Because most of the students who do not pass simply quit (AW, W, or don't take the last few exams) rather than complete the course, the GPA number does not include any students who didn't take the final exam whether they withdrew or not. Students who did not take the final are put in the "% who quit" category.

Notice there is a much higher withdrawal rate for the students in Calc I, but the performance of those who could handle the work was identical.

We see the same result in the second study. The withdrawal rates are slightly lower and the GPA is slightly higher than 5 years ago, but the GPA differences are not significant. The GPA for each group varies a lot from semester to semester.

For example, students taking Calc I in Fall 2003 had higher grades in physics (2.89) than those who had already passed calculus (2.64). The group that had passed calculus included quite a few who took the summer off and also had weak math grades. They lost their "edge" over the summer, and likely forgot the derivatives and integrals (not to mention the trig from a year or more earlier) they were expected to know perfectly on the first day of MAC2312. On the other hand, the students taking Calc I in Fall 2003 had A or B grades in trig and pre-calc and most had just finished taking both of those classes at the same time over the summer. They did well in both math and physics,

Update: Analysis of results for the 2004-2005 and 2005-2006 school years show the same trend. If anything, the situation may have gotten worse rather than better, with more students showing up whose "B" grade did not reflect learning the material.

Methodology

I examined the transcripts of every student who took PHY2048 in Fall '03 and Spring '04, sorting them based on whether or not they passed physics on their first attempt, and looked for a pattern. What a student knew when entering TCC did not seem to matter much at all. (Indeed, one group that started in MAT0024C had a very high success rate. Students who started in MAT0024 or MAT1033 and got an A can end up doing better than students who barely placed into MAC1105 and stuggled to get a C.) What eventually stood out was a C in either trig or pre-calc. These data say very clearly that students who did not earn at least a B in these relatively easy math classes are unlikely to have enough of those basic skills to pass physics.

I repeated the study in Fall '08 and Spring '09, primarily because I wondered about the effect of TCC's shift to an "early transcendental" approach to MAC2311. Because it puts all of the mathematics of the trig and inverse trig functions into the first semester, the "early transcendental" curriculum makes MAC2311 harder and much more dependent on knowing the properties of the trig and exponential functions and their inverses. It also makes MAC2312 a lot easier, so I wondered if this might change any of my results. I also wondered if anyone was paying attention to my warnings on the web, via various advising forums, and at the start of the semester.

The main difference between the first study and the second one is that I made a notation to indicate if a student had repeated trig. (I should have noted if they repeated pre-calc, but my focus was on trig.) This showed up in the "signal", so a repeat (even with a final grade of A) is now clearly in the at-risk category. This makes sense to me (having taught trig and calculus in my youth) because if abstract concepts like the logarithm and the domain of the inverse cosine function are difficult to grasp on the first try, a student might be expected to struggle with abstract concepts like the derivative of the inverse cosine function.

In both cases I excluded cases where a student was repeating PHY2048 in the spring semester from the cumulative data presented here. In the first study, I think I also excluded students in the fall semester who were repeats, but this is usually pretty rare. At one time I know I selected only those taking MAC2311 for the first time, but this was not done for the present study and I don't think it was done for the tables shown from the 2004 study.

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