BEST Calc- and Algebra-Based Textbooks with the same Chapter Sequence?

• Intro Physics
elleninphysics
Hi there!
I am teaching the algebra- and calculus-based physics courses at my university. The courses are taught at different times but in parallel, and students from both courses share the same lab sections. I'd like to keep them on the same content schedule without jumping around the textbooks, which can be frustrating for students.

I've fallen "out of love" with Halliday, Resnick, and Walker for the calc-based sequence. Most students who take this class at my university are chemistry majors or pre-medical/pre-vet/pre-pharmacy.

I've fallen "somewhat for" Cutnell & Johnson for the algebra-based sequence. Most students who take this class at my university are biology majors or pre-medical/pre-vet/pre-pharmacy.

Does anyone know of good, straightforward calc-based textbooks that align well with Cutnell & Johnson?

Thank you!
Ellen

MidgetDwarf
Most of the standard modern introductory physics books are similar. Maybe choose the cheapest option, so that students will spare money for beer/food?

PhDeezNutz, PeroK and Mr.Husky
Mentor
I've fallen "out of love" with Halliday, Resnick, and Walker for the calc-based sequence. Most students who take this class at my university are chemistry majors or pre-medical/pre-vet/pre-pharmacy.

I've fallen "somewhat for" Cutnell & Johnson for the algebra-based sequence. Most students who take this class at my university are biology majors or pre-medical/pre-vet/pre-pharmacy.
Welcome to PF.

Is that a typo where you have not differentiated much between the types of students that take the calc-based and algebra-based courses? It sounds like there are no Physics or Engineering students at your university?

Staff Emeritus
Why is it not possible to use a book slightly out of order: chapters 1-10, 15, 11-14, 16-20?

Homework Helper
Gold Member
In general, it's tough to match up textbooks from different authors...
different chapter sequences, different notations, different philosophies, different styles, etc...

You probably want to see the texts up close.
As a faculty member, you can certainly request a bunch of sample textbooks from publishers.

I've taught from many textbooks... but they're all so different (even though their coverages are similar).
Nothing comes to mind as a "calculus-based" version of Cutnell&Johnson.

Why is it not possible to use a book slightly out of order: chapters 1-10, 15, 11-14, 16-20?

Following @Vanadium 50 's suggestion, you could use a slightly out of order sequence... and you might be able to get a custom-published sequence from the publisher.

Of course, (although it would be a lot of work) you could develop your own materials, customized to your constraints. You start with your own "C&J supplements for Calculus-based students".

If you are willing to give up C&J, you might be able to find a textbook author you like
with both algebra- and calculus-based textbooks.
But even then, topics might not line up...

Here's Kinght:

 I. Newton's Laws 1. Concepts of Motion 2. Kinematics in One Dimension 3. Vectors and Coordinate Systems 4. Kinematics in Two Dimensions 5. Force and Motion 6. Dynamics I: Motion Along a Line 7. Newton's Third Law 8. Dynamics II: Motion in a Plane II. Conservation Laws 9. Work and Kinetic Energy 10. Interactions and Potential Energy 11. Impulse and Momentum III. Applications of Newtonian Mechanics 12. Rotation of a Rigid Body 13. Newton's Theory of Gravity 14. Fluids and Elasticity IV. Oscillations and Waves 15. Oscillations 16. Traveling Waves 17. Superposition V. Thermodynamics 18. A Macroscopic Description of Matter 19. Work, Heat, and the First Law of Thermodynamics 20. The Micro/Macro Connection 21. Heat Engines and Refrigerators ... https://www.pearson.com/us/higher-e...5th-Edition/PGM100003043413.html?tab=contents PART I Force and Motion Physics for the Life Sciences Describing Motion Motion Along a Line Force and Motion Interacting Systems Equilibrium and Elasticity Circular and Rotational Motion Momentum Fluids PART II Energy and Thermodynamics Work and Energy Interactions and Potential Energy Thermodynamics Kinetic Theory Entropy and Free Energy PART III Oscillations and Waves Oscillations Traveling Waves and Sound Superposition and Standing Waves ... https://www.pearson.com/us/higher-e...s-24-months/PGM100003050108.html?tab=contents

Gold Member
2022 Award
Who has invented this nonsense of a "calculus-free physics"? I think one of the most profound "inventions" of mankind has been the development of calculus. The fact alone that it was invented twice at the same time independently by Newton and Leibniz already shows that it's the natural language of (not only) the natural sciences!

The invention of "calculus-free physics", I guess by some "educationalists", is the most severe step backwards in the development of human culture!

PhDeezNutz, haushofer, dyn and 2 others
Gold Member
2022 Award
The problem is that the concepts cannot be formulated with some minimum of calculus!

ergospherical
Gold Member
2022 Award
That's philosophy not science!

Gold Member
2022 Award
Science of course!

ergospherical
Newton did a geometric based approach.
Yes, but have you ever sat down and properly grappled with some of these geometric proofs? They are as elaborate and perplexing as they are reflective of Newton's insane level of genius. Not anywhere close to a tractable approach for learning mechanics as compared to calculus (which becomes a necessity during even secondary-school mechanics).

Last edited:
berkeman, PeroK and vanhees71
Staff Emeritus
nonsense of a "calculus-free physics
The issue is that the alternative is not to teach these students calculus, but not to teach them any physics.

Last edited:
Hall
The problem is that the concepts cannot be formulated with some minimum of calculus!
But the problem comes when the student is not that mature to understand the concept of limit (and hence the foundation of calculus) but understands very easily the concept of instantaneous velocity or force is the [instantaneous] change in momentum.

So, if the institution focuses on teaching calculus (single-variable) completely before starting Physics course, it shall take them so long to reach Physics.

Gold Member
2022 Award
The issue is that the alternative is not to teach these students calculus, but not to teach them any physics.
No, the alternative is to teach the students calculus along with the physics. Nobody says that you have to teach calculus in the strict and formal way you teach it in a university lecture of mathematics majors. I can't imagine a better opportunity to start calculus than to introduce its concept together with the kinematical start of Newtonian mechanics.

You can start with the motion along a straight line (though in principle nowadays even the didactic experts think one should introduce vectors right in the beginning). Then you can discuss the concept of average velocity,
$$\langle{v}_{\Delta t}=\frac{x(t+\Delta t)-x(t)}{\Delta t}$$
and then it pretty straight forward to argue that to get the momentary velocity is to take the limit ##\Delta t \rightarrow 0##. Of course, this takes some time, but it is a more valuable insight than some unclear philosophical concepts about motion.

Homework Helper
Gold Member
Algebra-based physics, like it or not, is a reality.
We have a task to teach physics to students of all preparations.

Algebra-based textbooks have been pretty good, in my opinion,
getting the big ideas across without the calculus details.
We do give hints at the calculus by saying... "for a small displacement,..."

I think computations done iteratively can play a role in also giving hints at the calculus.
The physics of projectile motion isn't in the parabola.
It's in the part that says that:
at a particular instant,
the momentum-increment is equal to the net force multiplied by the time-interval to the next instant,
where the force happens to point downward with magnitude $9.8 m/s^2$.

Last edited:
vanhees71
Staff Emeritus
No, the alternative is to teach the students calculus along with the physics.
I disagree. More importantly, pretty much every college in the US disagrees with you and has not adopted your alternative. More importantly than that, this closes off access to physics to many high school students.

weirdoguy and robphy
Gold Member
2022 Award
We learned differentiation and integration in high school and also applied it to simple problems in physics. I don't see, why this should be a problem and what's the advantage of a more complicated representation without it.

Gold Member
2022 Award
Algebra-based physics, like it or not, is a reality.
We have a task to teach physics to students of all preparations.

Algebra-based textbooks have been pretty good, in my opinion,
getting the big ideas across without the calculus details.
We do give hints at the calculus by saying... "for a small displacement,..."

I think computations done iteratively can play a role in also giving hints at the calculus.
The physics of projectile motion isn't in the parabola.
It's in the part that says that:
at a particular instant,
the momentum-increment is equal to the applied force multiplied by the time-interval to the next instant,
where the force happens to point downward with magnitude $9.8 m/s^2$.
That's precisely what I meant above.

robphy
Staff Emeritus
We learned differentiation and integration in high school
So did I. Many US students don't. About 84%. Do we shut them out of physics?

We certainly can design a curriculum where the tippy top - and only the tippy top - students will thrive. I'm not sure this is a good idea.

PhDeezNutz and robphy
Gold Member
Do you know what percentage of algebra-based physics students pursue degrees in the hard sciences or engineering?

Last edited:
vanhees71
Homework Helper
Gold Member
Do you know what percentage of algebra-based physics students pursue degrees in the hard sciences or engineering?
No, I don't know.
However, in the places I have been at, there is an attempt to increase that number.

Staff Emeritus
Do you know what percentage of algebra-based physics students pursue degrees in the hard sciences or engineering?
Nope.

The typical flagship state offers three variations of the intro sequence: for physics majors, engineering majors, and pre-meds, with the last often algebra based. Is pre-med hard science? While this is a common set=up, it is not universal.

Homework Helper
Gold Member
So, if the institution focuses on teaching calculus (single-variable) completely before starting Physics course, it shall take them so long to reach Physics.
Even when calculus-1 and calculus-based physics are taken concurrently,
I find it annoying that
by the time we use "calculus" ideas in kinematics (early in Ch 2),
the calculus-1 class is only on sequences and series and convergence tests.

vanhees71
Hall
Even when calculus-1 and calculus-based physics are taken concurrently,
I find it annoying that
by the time we use "calculus" ideas in kinematics (early in Ch 2),
the calculus-1 class is only on sequences and series and convergence tests.
We have a live example of that frustration.

Gold Member
2022 Award
Even when calculus-1 and calculus-based physics are taken concurrently,
I find it annoying that
by the time we use "calculus" ideas in kinematics (early in Ch 2),
the calculus-1 class is only on sequences and series and convergence tests.
That's the usual dilemma. In the math lectures you have another goal, i.e., you teach really mathematics, and everything has to be formulated rigorously and theorems have to be proved etc. For the sciences, particularly physics, you need to apply calculus to describe (and I think there's no other way to describe!) Nature and do calculations with the goal to understand what's observed in terms of models and theories. That's why I think that you have to give the "math" in an "applicable, intuitive version" in parallel with the physics. The calculus-free textbooks I've seen seem also to introduce calculus without naming it as such, and then everything becomes much more complicated to express. Instead of introducing the idea of derivatives, you always have to argue with some limit ##\Delta t \rightarrow 0## instead of calling it a derivative.

Hall
The fact alone that it was invented twice at the same time independently by Newton and Leibniz already shows that it's the natural language of (not only) the natural sciences!
I don't know for how long Issac Barrow will have to be devoid of credit for inventing "the greatest discovery of human mind".

vanhees71
Homework Helper
Gold Member
Instead of introducing the idea of derivatives, you always have to argue with some limit ##\Delta t \rightarrow 0## instead of calling it a derivative.
Depending on the context, I might refer to something holding true
for "small displacements" or "short intervals of time",
hinting at but not explicitly saying ##\Delta t \rightarrow 0##.

If I really want to say derivative (but "can't"),
I instead say , for example, "slope of [the tangent line to the graph of] x-vs-t"
Often I'm interested in describing the behavior of the function,
not actually determining a value of the rate.
If I need to convey the ##\Delta t \rightarrow 0## idea,
I show a desmos plot of the function, centered at a point of interest,
then zoom-in until it looks like a line in my viewport.
Then I tell the students, "I want the slope of that line-- the tangent line at that point".

Gold Member
2022 Award
Yes, and that makes the whole description less easy to express and to understand. Why do you forbid to call a derivative a derivative? Of course all these intuitive meanings are very important particularly for the scientist who wants to apply mathematics to the description of the real world, but why should it be easier not to introduce a general concept summarizing all these meanings making it to a versatile tool for all kinds of applications?

Geddyleesbass
But the problem comes when the student is not that mature to understand the concept of limit (and hence the foundation of calculus) but understands very easily the concept of instantaneous velocity or force is the [instantaneous] change in momentum.

So, if the institution focuses on teaching calculus (single-variable) completely before starting Physics course, it shall take them so long to reach Physics.
True. One must develop a love for the subject and the mathematics will follow.

Hall
MidgetDwarf
Yes, and that makes the whole description less easy to express and to understand. Why do you forbid to call a derivative a derivative? Of course all these intuitive meanings are very important particularly for the scientist who wants to apply mathematics to the description of the real world, but why should it be easier not to introduce a general concept summarizing all these meanings making it to a versatile tool for all kinds of applications?
Yes, it causes more frustration by not calling it a derivative. No need to give the formal definition of a derivative. Just a simple curve in the xy-plane showing different secant lines between a stationary point, and the other that moves. Then make the points closer and closer to show the secant line now "becomes" a tangent line. You can do a velocity example. Its really not that difficult. If students have issues with this simple example, then maybe the students should wait to take physics.

vanhees71