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thharrimw
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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.
Work as a line integral;
the rocket equation;
coupled, damped, and forced harmonic oscillators;
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?
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.
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?
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?
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.
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?
Say what? That's the definition of acceleration. How does it follow from Newton's second law?
I don't know much about cal. based physics but, I'm guessing it comes from 1/2 a^2 +m
I think D H is talking about this version of Newton's second law [tex]F=\frac{d(mv)}{dt}[/tex]. I'm not sure how [itex]\ddot{x}=a[/itex] comes from this though; perhaps I'm missing something!Say what? That's the definition of acceleration. How does it follow from Newton's second law?
That makes absolutely no sense. And the units don't match up either.