Unofficial Advice
on math needed for
"physics with calculus"

from Dr. James Carr
Office: SM 290
Phone: 201-8971
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Office hours   can be found here   along with E-mail addresses

Last Updated: 19 August 2010
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Success in physics depends on your ability to do four 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.

(4) Compute the answer accurately and round the result properly.

Of these, 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 (students who earned only a "C" or needed to repeat the class) are likely to fail physics and/or calc I on their first attempt. [This does not apply to students who earned a "C" in TCC's honors MAC2147 (combined trig and pre-calc) class.] 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 really 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" may not be 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 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.

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Some Key Recommendations

(A) Students in the AS engineering program should complete Calc I before enrolling in PHY2048 unless they got an A or B 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) Other students should think three times before taking MAC2311 and PHY2048 at the same time if they earned a C in either MAC2140 (pre-calc) or MAC2114 (trig) or had to repeat one of those classes. Many students with those grades do not succeed in physics while taking the first semester of calculus. [The only exception is that students with a C in MAC2147 at TCC do OK.] 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. set up a schedule that includes 1 hour every weekday at the Learning Commons in addition to setting aside 3 to 4 hours every day (including weekends) for calculus and physics homework.
I also advise you to consider taking PHY2048 and Calc II (MAC2312) separately if you did not get at least a B in MAC2311 or don't remember everything you "knew" when you took your Calc I final exam. Once you are past Calc II, there is usually little problem taking PHY2049 with Calc III (MAC2313) if needed. In fact, those two courses work very well together.

(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 needed 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!

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The Data - Success Rates

My recommendations are based on hard data, not guessing.

There were two studies done, one in the 2003-04 school year (when TCC used the "late transcendental" curriculum), and a more extensive one during the past two school years (2008-2009 and 2009-2010) where TCC used the "early transcendental" curriculum. This curriculum has many advantages for students taking physics, but it puts a greater premium on knowing the properties of the trig, inverse trig, and log functions in Calc I.

In these tables, "pass" means an A, B, or C grade in PHY2048. The ratio is based on all students, so "fail" means a grade of D, F, or W. What I want you to notice is that the students who survive calculus despite coming in with a weak background in pre-calc or trig have learned what they didn't get the first time and do better in physics as a result. However, 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. That is why we keep MAC2311 as a co-requisite for PHY2048.

In this first table, covering two school years and several hundred students, a student is only in the "A" category if they got an A in both trig and pre-calc on the first attempt. Students in the "B" category might have gotten an A in one class and a B in the other, but again on the first attempt. The "C" category includes students who needed two or more attempts to pass these classes (regardless of what grade they got) as well as students who earned a high grade in one class and a C in the other on the first attempt.

Statistics for 2008-2009 and 2009-2010 school year
Lowest Grade in
pre-calc or trig
Fraction that pass
if taking Calc I
along with physics
Fraction that pass
if passed Calc I
before taking physics
A 85% 100%
B 62% 77%
transient student
or placement
directly into calculus
no data 67%
C or
repeated class
37% 56%

The "placement directly into calculus" group includes students with AP credit for MAC2311, placement with the TCC CLM exam, and cases where some other college or university allowed a student take calculus directly out of HS, but also includes transient students where we only know that some other college says they met the requirements for this course.

In the second table, from my initial study in the 2003-2004 school year, no distinction was made between students who got a B in trig on the first try or had to repeat the class one or more times before earning a B. It also represents a significantly smaller sample of students.

Statistics for 2003-2004 school year
Lowest Grade in
pre-calc or trig
Fraction that pass
if taking Calc I
along with physics
Fraction that pass
if passed Calc I
before taking physics
A 100% 100%
B 64% 78%
transient or
placement directly
into calculus
no data 64%
C 11% 36%

You might notice that the survival rate of "C" students used to be extremely poor. There is a reason for this. I told my math colleagues about this result and we discussed some of the areas where students seemed particularly weak. The calculus instructors did the same thing, because the same students who failed physics usually failed calculus. The result is that students who pass trig and pre-calc with a C have a fighting chance to pass both classes despite the fact that MAC2311 is harder than it used to be.

My thanks (and yours, I trust) to my math colleagues for this improvement. Many more students have gotten the message that they will need to remember this material, and improved success has been the result.

One other thing I can see in the data is that MAC2312 used to be a lot harder than MAC2311. Although MAC2312 is still harder than MAC2311, the difference in difficulty is much less than it used to be.

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.

The withdrawal rate for students taking MAC2311 is much higher (40 to 50%) than the withdrawal rate for students who have passed MAC2311 (20 to 25%) before taking physics. The higher numbers were from 2003-2004, another sign that students are better prepared today than they used to be.

The result I found most interesting, however, was that the GPA of the two groups was almost identical if we look only at students who completed the course by taking the final exam. There is no indication at all that students who have passed MAC2311 get higher grades than the ones taking MAC2311 at the same time as PHY2048. There have been semesters where the students taking MAC2311 had higher average grades, and ones where they were lower, but they are almost the same when averaged over several semesters.

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