Applications of differential equations in geometry, percentage calculus and physics - need references

Question

I am looking for references and free online books of solved problems in these topics. By applications in geometry I mean something like this

article about applications of integrals (something of that difficulty).

By applications in physics I mean simple classical mechanics (velocity, acceleration,...), combined with geometric representation.

Applications in percentage calculus should also include geometric representation.

Could someone suggest some good references and free online books with solved problems?

Answer 1

You might want to look into the Lagrangian, as that can spit out some nice differential equations. I'll let Wikipedia do the explaining: https://en.wikipedia.org/wiki/Lagrangian_mechanics.

If you like that, I suggest looking up Morin's Introduction to Classical Mechanics. It has some great stuff in there. I think the fourth chapter or so is on the lagrangian.

There are plenty more applications of differential equations, however. Whenever we want to model any process over time, we have to use a differential equation (I hope you see why a differential equation may be useful in that regard). ODE's are used across all the Sciences, and so they show up everywhere.

Answer 2

For application of percentage you can check following links. Both provide basic and advance concepts with few examples.

1. Solving problems with percent

2. Applications of percentage

For Applications of Physics you can see following link -

1. Concepts in Physics

For calculus -

1. Concepts of Calculus with detials

One last thing you need to search things piecewise because I think that helps you in understanding each topic deeply. Like you want to learn concept of velocity with examples and problems. Search only for that. Because there are so many links and in each link you can get something new. You can make list of topics you want to learn.