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in my high school physics class we are doing algebra baced physics but i have heard of calculus based physics and i wanted to know the differences between them and the different Applications that they have.
I just dusted off my very old Halliday and Resnick, copyright 1966, and they certainly went well beyond algebra-based physics. Here are a few topics in which calculus played an integral role: Work as a line integral; the rocket equation; coupled, damped, and forced harmonic oscillators; simple fluid dynamics and thermodynamics. Moreover, many topics which are presented as givens in pre-calculus physics are derived in that ancient version of Halliday and Resnick; e.g., Kepler's laws of motion. Has the Halliday, Resnick, and Walker text dumbed things down since I went to school back in the stone age?Adding calculus to Physics I, at least at the level of Halliday, Resnick, and Walker, results in hardly any new physics being taught.
This is presented, but in the exercises students are only asked to integrate along straight line segments. And for most exercises, no integration is required at all.Work as a line integral;
This is presented, but students don't actually have to do any calculus in the exercises.the rocket equation;
The differential equations for these systems are presented, as well as their solutions. But they don't solve the equation in the book, and the students are never asked to do it. A curious student could plug the given solutions back into the diff eq to verify that it is indeed a correct solution, but this is never asked of the student.coupled, damped, and forced harmonic oscillators;
The syllabus at the school where I taught as a grad student excluded these topics, as full courses in each subject were offered. So I never went through these chapters of H&R.simple fluid dynamics and thermodynamics.
In this context, derivation is "a sequence of statements (as in logic or mathematics) showing that a result is a necessary consequence of previously accepted statements" (from http://www.merriam-webster.com/dictionary/derivation" [Broken]).ok all of this has made me more confused,
What is derivation?
This is a differential form: [itex]\nabla \cdot \mathbf{B} = 0[/itex]. The corresponding integral form is [itex]\oint_S \mathbf{B} \cdot d\mathbf{S} = 0[/itex]. In English, there are no magnetic monopoles. If you haven't had calculus, that looks like gibberish.What is a differential form?
and
What is a integral form?
Yes. That is one of the reasons we use it.also in calc baced physics can you use these differntial and integral things and do more then you could if you used algebra equations?
Some curricula don't require calculus-based physics, let alone requiring calculus.Why do educators still teach algebra-based physics when they could simply teach the calculus mathematics first, then afterwards go straight to calculus-based physics? It saves the trouble of having to memorise equations when doing algebra-based physics.
Some high schools don't require physics [unfortunately]... and, if it is offered, it won't be calculus-based since calculus would be taught in the senior year, if at all. (If the high-school follows a "physics-first" curriculum, it certainly won't be calculus-based.)Curriculum for high school or college? Calculus is an essential mathematical tool for just about every scientific, engineering field. And why don't require it when just about every student in high school is going to have to learn calculus anyway, unless they've chosen to major in the arts and literature?
My high school didn't require us to take calculus (I did anyway, apparently I was a year ahead of everybody or something). The "regular" track ended with trig.Curriculum for high school or college? Calculus is an essential mathematical tool for just about every scientific, engineering field. And why don't require it when just about every student in high school is going to have to learn calculus anyway, unless they've chosen to major in the arts and literature?
I don't think there's any more equations to remember. The constant acceleration equations are used so often in introductory physics, calculus or not, that it's useful to remember it anyway. I don't think there's much more to remember.Why do educators still teach algebra-based physics when they could simply teach the calculus mathematics first, then afterwards go straight to calculus-based physics? It saves the trouble of having to memorise equations when doing algebra-based physics.
Say what? That's the definition of acceleration. How does it follow from Newton's second law?It can be derived from [itex]d^2x/dt^2 = a[/itex], which in turn is a consequence of Newton's second law.
I just dusted off my very old Halliday and Resnick, copyright 1966, and they certainly went well beyond algebra-based physics. Here are a few topics in which calculus played an integral role: Work as a line integral; the rocket equation; coupled, damped, and forced harmonic oscillators; simple fluid dynamics and thermodynamics. Moreover, many topics which are presented as givens in pre-calculus physics are derived in that ancient version of Halliday and Resnick; e.g., Kepler's laws of motion. Has the Halliday, Resnick, and Walker text dumbed things down since I went to school back in the stone age?