College Physics vs University Physics: What Is the Difference?
This lesson discusses one of the most common questions asked by STEM students:
What is the difference between College Physics and University Physics?
The lesson compares algebra based physics and calculus based physics textbooks and explains why the differences are often smaller than students expect. :contentReference[oaicite:0]{index=0}
The Two Common Physics Sequences
Most colleges offer two introductory physics sequences:
- College Physics (Algebra Based)
- University Physics (Calculus Based)
These courses generally cover the same fundamental topics:
- Mechanics
- Energy
- Momentum
- Rotational Motion
- Oscillations
- Waves
- Thermodynamics
- Electricity
- Magnetism
- Optics
The primary difference is how the concepts are presented and derived. :contentReference[oaicite:1]{index=1}
Most students are surprised to learn that the actual problem solving process is often very similar in both courses.
Algebra Based Physics
In an algebra based physics course, students are usually given the final formulas and taught how to apply them to solve problems.
For example:
The emphasis is placed on:
- Understanding physical concepts.
- Unit analysis.
- Algebraic manipulation.
- Problem solving.
- Applications.
Students generally use formulas directly without spending significant time deriving them using calculus. :contentReference[oaicite:2]{index=2}
Calculus Based Physics
In a calculus based course, students are often shown where the formulas originate.
Instead of simply presenting the final equation, the textbook may include derivations involving:
- Derivatives.
- Integrals.
- Differentials.
- Vector notation.
- Multivariable concepts.
The final formulas frequently look identical to those found in the algebra based version. The primary difference is that the textbook includes the mathematical development leading to the result. :contentReference[oaicite:3]{index=3}
Point A to Point B
One of the central themes of the lesson is that calculus based physics often shows the mathematical steps connecting an initial idea to a final formula.
The algebra based text may simply present:
while the calculus based text explains the intermediate mathematical reasoning that connects the two. :contentReference[oaicite:4]{index=4}
The calculus book often explains where the formula comes from. The algebra book often focuses on how to use the formula.
Do You Actually Use Calculus?
A major point made throughout the lesson is that many introductory calculus based physics courses still spend most of their time solving problems with algebraic equations.
Students frequently:
- Substitute values.
- Rearrange formulas.
- Perform unit conversions.
- Solve systems of equations.
- Interpret physical situations.
Even in calculus based courses, the actual homework and exam problems often resemble those found in algebra based courses. :contentReference[oaicite:5]{index=5}
Where the Calculus Appears
Calculus becomes most visible when deriving equations and discussing advanced physical concepts.
Examples include:
- Work as an integral.
- Electric fields.
- Potential functions.
- Continuous charge distributions.
- Line integrals.
- Vector calculus concepts.
Many of these ideas are connected to Calculus III and Vector Calculus, topics students often study after beginning introductory physics. :contentReference[oaicite:6]{index=6}
Why the Notation Looks Scary
Students are frequently intimidated by symbols such as:
The lesson encourages students not to panic when encountering unfamiliar notation. Often the notation is being used to explain the origin of a formula rather than introducing a completely new method of solving the problem. :contentReference[oaicite:7]{index=7}
Additional Topics in University Physics
Many university physics texts contain additional chapters and more advanced discussions.
These extra chapters may include:
- Advanced electromagnetism.
- Vector fields.
- Continuous systems.
- Modern physics topics.
- Additional mathematical derivations.
This is one reason university physics textbooks are often significantly longer than algebra based physics textbooks. :contentReference[oaicite:8]{index=8}
Final Thoughts
The difference between College Physics and University Physics is often smaller than students expect. Both courses teach the same physical principles and many of the same problem solving techniques. The primary distinction is that university physics typically includes the calculus based derivations behind the formulas and introduces additional mathematical notation and advanced topics. Students should focus on understanding the concepts rather than becoming intimidated by the notation itself. :contentReference[oaicite:9]{index=9}
Original Transcript
All right, kids. I’m gonna I’m going to show you guys here the difference between college physics and university physics. I’m going to be going through and doing a crash course on all this uh all the physics chapters and sections for you guys. Just a quick little I’m just going to take questions and answer them real quick the way you would on an exam to just show you guys how you should be ultimately the goal of how you should be thinking. I’m not trying to do your homework for you. I’m not trying to help you cheat. I’m just showing you how you should be thinking as a scientist. I’m trying to prove to the uneducated kids that have the biggest egos on the planet that know nothing about nothing that they are wrong about everything. It’s very difficult to prove to somebody that knows nothing that they’re wrong about everything. It’s amazing how people that know nothing think they know everything. The the less you know, the more you know. And the more you know, the more you you realize you don’t know anything. So, make sure you ask your college STEM major everything while they still know everything because by the time they hit senior year, they’re going to realize they don’t know nothing. [laughter]
So what is the difference between the college algebra and the calculus physics? The algebra based physics or calculus base which is college physics versus university physics. Here’s the college physics. Hugh young university physics. Hugh young college physics. Same setup. Look. See how this coloring color schematic scheme all looks the same. There are 30 chapters in the college physics. There are 44 chapters in the university physics. They’re all the same. They’re all the same. It’s all the same. Like, there’s no difference. And the calculus is as much present in this book as it is in the calculusbased book. This is only a preview of the book, but the um the calculus they put the calculus stuff in this book just as much as they do in the um in the non in the calculus in the actual calculus one. They they put they put the same stuff in it. It’s just um I can’t find a I can’t find an open- source version. of the college algebra the college physics book by Hugh Young. So I might have to buy it from Amazon. Uh maybe this one is this one’s a little this one’s a different author but uh this is the full book. So mechanics thermodynamics this this one has 30 chapters same as the other one. So I’m I’m going to go ahead and download this one. I’ll use this one. So college physics this will be book 29 in my book here. And then I want to site this book. So, I’m going to have Chat GPT site this for me real quick. Uh, site this book.
Site this book. And I can add it then to my to my citations for my textbooks that I’m collecting here. So, under my textbook, my textbook collection for references and sources and stuff
is this is book 29. And let me get my citation. It doesn’t matter what citation I’m using. There this is not there’s not a formality here. And then I want the link that I found it from for legality reasons. And there we go. Okay. So, that book’s been cited. So, that book’s got the same issue, the same thing with 30 chapters. Um, but the point is why I’m downloading this, why I want to show you this is because in the in the algebra book, let’s see if they if they do the same thing in this algebra book. If I just go to like if I just go to like laws and motions or something and I I want to take a look at their theorems. This is the algebra based book. And I want to just take a look at how they’ve written their theorems. And so they’ve got this summation here that that’s not necessarily calculus, but it usually comes in calculus a little bit more prominent than it does in non-calculus. Uh but uh let’s just let’s just see this guy. The font he used in this book is terrible. Uh, I don’t like the choice of font, but I just I want to see in the algebra book if they introduce calculus in here because derivative because they they in the in the Hugh Young I do remember looking through the Hugh Young algebra book and it seemed like it seemed like they they did integrate the I don’t have access to that book though. Come on. Okay, stop already. I don’t have access to the Hugh Young book. But in this book here, it doesn’t look like they are incorporating phys uh calculus notation. They’re not actually doing calculus in the algebra book, but they’re incorporating calculus notation in uh some of the problems, but they’re not actually doing any calculus. And it in in all honesty in the actual calculus book itself they um they don’t really do any calculus cuz all of these equations what you guys see here all of these equations they’re essentially all derived using calculus. So even though you’re in the calculusbased subject you’re still just doing these equations. So let me show you. So here this is the algebra based this is chapter whatever chapter chapter 5 algebra based. So, let me go to the calculusbased one here. And I go to chapter five in the calculusbased or any chapter. I just want to show you the difference between the books and the notation. So, so here, do you see here where um where was that? I was just at where is that box I was just at? Right here. Okay. You see this right here? This is the calculus. This is an anti-derivative integration definite integral. This this is a uh a line integral situation. This is something you would learn in calculus 3. So, this this is something you’d learn in calculus 3 level. But here’s the thing. Do you see this equation here? And you see this equation here. In this book, they are showing you how V is equal to this in the algebra book. They’re just showing you the equations. They’re not showing you the calculus derivation. You’re not actually going to use the calculus derivation. You’re going to use the algebraic derivation. Do you see this here? This is this is your basic equation. This is the exact same kind of equation that is in the algebra based book. It’s the same thing. Here it is. There’s your same equations right there. And this same equations, this is chapter 23, electromagnetism stuff. But basically the difference between the two books is is there’s a 14 chapter um discrepancy between the two. And then in this book they show you the calculus in between going from A to B. So from A to B, they show you the calculus in between. Whereas in this book they just show you A and B. They don’t show you the calculus in between. So in in in uh in the problem solving when you do the problem solving in the calculus you’re not going to do any calculus. They show you the calculus here. This is the differential dv and dy the differential. They show you the the um derivation of the formula. You don’t actually need to know how to do calculus to do the calculus based physics. You’re just going to be confused about what’s in between a and b. You’re going from a to b. They’re just showing you everything in between it in the calculus book. So, it’s really not it’s really not any different. But those extra 14 chapters are going to introduce a little bit more of calculus related stuff where you have to use calculus, more advanced stuff. But the thing is is that you guys take physics one and physics 2. Most of the stuff in the physics book comes from the third year of calculus and vector calculus. You won’t even get to that until you finish physics. So, most of this is going to be very confusing. This right here, you won’t understand what this means until calculus 3. and you’ll be introduced to it co-requisite calculus 2 with university physics [snorts] that my point is is that don’t be scared of the notation because it doesn’t really mean anything. All they’re doing is going from point A to point V B. They’re showing you this is all the calculus then they’re showing you the end result of what you’re going to use in the equations. That’s the that’s there’s really no different there’s really no not any difference between the algebra and calculus based standard undergraduate twopart series. It’s really the same exact thing. I’ve I’ve taken both of them. I’ve tutored people through both of them. I’ve seen them from all kinds of universities. It’s all the same questions. You do the same exact thing. Rarely do you actually do any calculus in a calculus based one unless you’re in like an honors course or something. But that’s a difference.