How is Physics taught without Calculus?

[Will Flannery]

"Regarding simulation: time should not be wasted in core physics classes on simulations."

If we step back a minute, what is physics? Ans: creating mathematical models of physical systems and analyzing the model to be able to predict how the physical system performs.

In classical physics, the models are sets of differential equations. and ideally the model is analyzed by solving the differential equations. Given the solution, we can predict how the real system will perform.

However, the differential equation models of most physical systems are not analytically solvable. Thus, we read in 'Deep Learning for Teaching Physics to Computers' (satirical but accurate) by former AJP Editor R. Price "At Crenshaw-Mellon University,9 in fact, simple computer programs have been developed to recognize and solve the dry-sliding-friction-block-on-tilted-plane, ballistics, and pendulum problems that constitute almost all of university physics."

What are the goals of simulation? The goal of a simulation of a physical system is predicting how the real system performs. What does a simulation start with? It starts with a differential equation models of the system. So, the goals of the classical analysis of a physical system and the simulation of the system are the same. The difference is that simulation can be used to analyze analytically unsolvable systems. That is why computational calculus, i.e. simulation, has been the norm for the analysis of physical systems since the mid-20th century.

 

[Mister T]

Up until about 1960 or so the introductory college-level sequence for physics majors was taught without the use of calculus in America. To the uninitiated using calculus to introduce physics is rather like using magic. Students, on average, show little comprehension of even the most basic concepts and instead rely on memorization to pass tests. Anyone who has ever taught introductory physics, with or without calculus, will recognize this affliction.

Edit: If you look at the textbooks used prior to about 1960 to teach introductory college-level physics to physics majors you will see that they rather resemble the noncalculus introductory college-level physics textbooks used today.

 

[gleem]

Up until about 1960 or so the introductory college-level sequence for physics majors was taught without the use of calculus in America.

Huh! The text I used in 1960 was by Shortey and Wiliams published in 1955 meant to be used with a concurrent course in calculus. I know this text was used by Wheeler at Princeton. Since the college that I attended was of no particular national importance I find it hard to believe that physics was routinely taught without calculus to physics majors during this time.

From the preface of the Australian edition of Sears and Zemansky University Physics

When the first edition of University Physics by Francis W.Sears and Mark W. Zemansky was published in 1949, it was revolutionary amongcalculus-based physics textbooks in its emphasis on the fundamental principlesof physics and how to apply them

 

[Mordred]

You would be surprised. For example the high school I attended didn't even offer Calculus. I ended up taking it as an option when I went to University. Glad I did as I needed it for Particle Physics.
Though not as much for Cosmology or Astrophysics. (Never took Astrophysics for the record). That was a good 35 to 40 years ago though lol.

Now I meet students that graduate that cannot divide fractions

 

[Mister T]

Huh! The text I used in 1960 was by Shortey and Wiliams published in 1955 meant to be used with a concurrent course in calculus.

I remember reading this in a journal years ago but must have got the year wrong. Perhaps by several decades.

I used the same text in 1973-74. The professor didn't use calculus even though it was a co-req. I also took calculus and a calc-based physics class my senior year in hs.