Calculus-Based Physics

Understand and get comfortable with the understanding of calculus.

Once you understand the patterns, you can visualize when and were to applying them.

I don't believe there is a magic bullet for what you want.

Some books for calculus do include some exercises to practice applications. But, as they should not consider the learner a specialist in any field of knowledge, I guess, they do not include a wide repertory of them. Some guys learn calculus just to go on maths, others in very different fields.

At the end, you should look at Physics books looking for practical exercises to apply calculus. Randall Knight? I confess I am not familiarized with him, but have you checked out Halliday-Resnick's Physics? Basic book for physics in engineering around here, used to include a lot of exercises, from the easiest ones to the deeper ones.

At least, by the time I was in the university (mech. eng.), those were the ones that used to apply calculus at most in the early begining of engineering. The rest was just maths, long nights and low grades in tests. It's life...

I enjoy how Halliday-Resnick's provides somewhat of a 'bigger picture' perspective of material as displayed through the excercises and examples. Simple and associative presentation of concepts. Great reference material.

Thanks bhrescobar !!!

As we say here in Pittsburgh, "You can't expect to buy gasoline at Isaly's (a local deli known for chipped ham)."

You should not expect to find that sort of problem, i.e., the strength of an electric field due to various shaped charges, in a General Physics book. Due to time restraints, and the need for prerequisites and corequisites, problems of that complexity need wait for further study. Knight is an excellent book as are Halliday and Resnick 1st ed and 2nd ed (after that, H&R goes downhill), but for advanced (complex) problems in E&M, you might want to go to something like Landau and Lifschitz.

Hurray, someone else uses Landau and Lifschitz too.

Thanks for the input. I am looking into finding those books. Of importance to me is to do problems that require the application and the happy marriage of mathematical and physical concepts. Thanks again.

Any good basic EM Theory textbook should get you started. For more advanced topics, try a google search for the following keywords/topics to see if the results fit your needs.

"Method of Moments in Electromagnetics"

"Computational Electromagnetics"

I did some computational electrostatics for my thesis and was able to find a closed form expression for the electric field at some point in space due to a uniformly charged rectangular planar area. I began with the method of moments. My instructor(s) referred me to Harrington's "Time-Harmonic Electric Fields". I'd be happy to pass these results on to someone who would have use for them.

Top answer. Especially; "none of the content of Maxwell's equations is specifically about electromagnetism" and "it's all about the geometry!"

"Once you have the geometric ideas and methods clear in your mind, you can apply them"

Stirling advice; you have my vote.

If you mash them up together while learning them, you will only confuse yourself

My experience is that learning by association instills concepts and ideas with a sense of conviction that breeds the confidence for application in a real-world scenario. I can see the disjointed nature of science and math, however, whenever an opportunity for analogy arises I am more than enthusiastic to seize it:

Theory of gravity and Coulomb's law are both inverse square laws involving properties of two interacting particles and a constant. They differ in that gravity is always attractive whilst Coulomb's can be either attractive or repulsive.

I found it a good cognitive reinforcement after establishing that the change in momentum and change in kinetic energy can be concurrently visualized as Impulse and Work respectively.

You've just illustrated my point very well, thank you.

The inverse square law follows from the ratio of the surface areas of concentric spheres of different radii, together with Stokes' theorem stating that the net flux of any quantity through a closed surface is proportional to the net source or that quantity in region enclosed by the surface.

So you see, it's all about geometry.

No particles, charges or masses required.

Correction: "the net source or that quantity" should read "the net source of that quantity".

Another correction: "in region enclosed" shoud read "in the region enclosed" so, with both corrections, the statement of Stokes' theorem becomes "the net flux of any quantity through a closed surface is proportional to the net source of that quantity in the region enclosed by the surface."

Guest, I'd be pleased to see you sign in. That was a very good summary.

Sorry for posting a reply so late to this topic.

I'm not clear from the OP whether there is a need for learning calculus or just applying the calculus you already know to specific problems. That might help people suggest routes and resources.

I am extremely impressed by the quality of information available on this site. I beleieve at the heart of engineering is the ability and willingness of participants to share information. You guys are great!!!

Thank You all.

Our instructor used a book called the very same: "Physics for scientists and engineers."

but written by an author by the name of Giancoli, and it contains shaped-charge problems. It comes in one book as a three-volume set, but most of the electricity problems appear in the second and third volumes. I don't know if you could purchase those separately or not. Good luck!