For example, for the derivation of the gradient, divergence and curl formulas of the curvilinear coordinate system (cylindrical and spherical coordinates), there are intuitive but not too strict derivation methods, which are easier to remember.There are other derivations that focus on mathematical formality and are not very motivated, and that kind of derivation is easily forgotten.hutchphd said:How does one learn to play the piano? Start with simple songs and practice practice practice.
Thank you for your advice.hutchphd said:Unless you use them ( or have a brain very different from mine ) you will forget the details. But it you will remember their existence and could reproduce them (with effort). So better to solidly learn the elementary things, in my opinion. This means practice using them to solve problems for me.
Are you studying a physics course or a math course? In the US at least, the "intuitive but not too strict" methods are satisfactory for a physics course, but math courses (taught in a math department) tend to demand more rigor.Passers_by said:For example, for the derivation of the gradient, divergence and curl formulas of the curvilinear coordinate system (cylindrical and spherical coordinates), there are intuitive but not too strict derivation methods, which are easier to remember.There are other derivations that focus on mathematical formality and are not very motivated, and that kind of derivation is easily forgotten.
I'm taking a physics course. I'm not saying that the intuitive approach is bad for a physics course. What I'm trying to say is this---Some formulae in books are derived in a more mathematically skillful way. The derivation in this way is not easy to remember.jtbell said:Are you studying a physics course or a math course? In the US at least, the "intuitive but not too strict" methods are satisfactory for a physics course, but math courses (taught in a math department) tend to demand more rigor.
constant rereading in practice. For mechanics, a lot of the derivations of the formulas are geometric in nature. so drawing an ideal diagram helps with the derivations. However, depending at the level of the course and the demands of the course, it may be overkill.Passers_by said:How did you find PF?: The Internet search
I tend to forget the proofs of theorems, the derivations of formulas and the content of equations in books. What should I do?
Things like the generating Function of Legendre Polynomials. The proof of the identity is very tricky. Close the book, and after a while, I'll forget the art of dealing with problems.MidgetDwarf said:constant rereading in practice. For mechanics, a lot of the derivations of the formulas are geometric in nature. so drawing an ideal diagram helps with the derivations. However, depending at the level of the course and the demands of the course, it may be overkill.
I think its more important to know the statements, what are the conditions and under what cases they work, and what can they applied/used for.
What level classes are you at? intro? Junior? Senior?
Have a look at Alonso and Finn: Fundamental University Physics. Most things are derived and in general form. Not too many diagrams, but the diagrams that are in the book are memorable. Great and concise explanations.
if something more advanced, look at Taylor Mechanics. A bit more talkative, but Taylor does explain the why.
I did a dual major in math (pure)/physics, so I won't say much more. I will let more experience members chime in.
Ahh. The one that requires using the binomial theorem to expand the denominator? I would say in order to understand this. Is to a) memorize the identity , b) know the binomial theorem and use it to expand the denominator, c) the left is actually an alternating series. d) rearrange the terms (maybe memorize what the result should be like).Passers_by said:Things like the generating Function of Legendre Polynomials. The proof of the identity is very tricky. Close the book, and after a while, I'll forget the art of dealing with problems.
I've given just one example here. It's the kind of thing that I tend to forget how the writer dealt with it. Physics is described in mathematical language, so sometimes I don't strictly distinguish between the two subjects.MidgetDwarf said:Ahh. The one that requires using the binomial theorem to expand the denominator? I would say in order to understand this. Is to a) memorize the identity , b) know the binomial theorem and use it to expand the denominator, c) the left is actually an alternating series. d) rearrange the terms (maybe memorize what the result should be like).
So to understand this at the bare minimum, the things I listed are key. You may need to look at the binomial theorem and alternating series facts..
You can also do it with dipole moment generating function.
The key idea, is to think about it, rewrite it many times, and solve problems. When you move onto higher courses, you may forget little tidbits. Thats where constant review comes into play, and knowing what to review/learn becomes second nature if done consistently.
Maybe its more of an issue with mathematics itself?