So can any of you mathematician help show me examples of applying

>>8568657
Read:
Taylor - Classical Mechanics
Griffiths - Introduction to Electrodynamics
Shankar - Principles of Quantum Mechanics

>>8568662
Do you think its possible to find them free
online?

>>8568657
>no friction, massless object, 100% efficiency
who said it's not important to know the problems in the ideal case? This prescribes an "upper limit" to the potential output.
Furthermore, you'll learn applications when your core courses bring out something and say "you should have learned this in your vector calculus class" or something.

Get over yourself

>>8568675
I should mention that it's also not possible to go into super detail during lecture for a digression, the prof needs to get through the material.

>>8568662

> Taylor - Classical Mechanics
http://alemanlab.uoregon.edu/files/2013/12/Taylor_Chapters_1-2-1gl2iff.pdf

> Griffiths - Introduction to Electrodynamics
http://117.55.241.6/library/E-Books/Electromagnetics%20by%20Griffiths.pdf

> Shankar - Principles of Quantum Mechanics
http://home.basu.ac.ir/~psu/Books/%5BRamamurti_Shankar%5D_Principles_of_Quantum_Mechanic(BookFi.org).pdf

Here's what I found, the taylor one seems short, are these it?

>>8568675
>>8568676

I never really thought of that, they cant go into detail, but a problem that shows how to do it would be very helpful, and in my opinon, would incite an eagerness to learn more from students, wouldnt you agree?

Yea, its nice to know ideal and upper limits but what good is it if I need an exact answer or extrememly close approximation. What if i need to find where a projectile lands, sure, I'll know where it landed ideally but it probably didnt land really close to the ideal spot. you know?

>>8568665
Everything can be found free online. Specially something so mainstream it is posted here.

>>8568688
are you the same anon? Some things usually cost money, was just wondering. though I still went and looked for them. if you are the same anon, can you verfiy my links above?

>>8568685
you'll quickly learn that nothing even slightly complicated in science or mathematics is 100% exact, and that approximations are a necessity.

in fact, you might find that often we don't even want exactness, we just want to get close enough for it to have meaning.

take for example the structure of a molecule. i'm sure you've heard of electron orbitals and how they interact to form bonds and create chemistry.

but we can also use advanced mathematics with computational quantum mechanics to solve the exact energy of the molecules (using thousands of "approximations"), which gives us a 100% unique solution to the schrodinger equation, and so a 100% unique "picture" of the molecule.

the problem is in achieving exactness, the concept of orbitals is abandoned, and instead electrons become a purely mathematical construct (ie we can no longer relate the energies to any classical idea such as the modes of a vibrating string, electrons localizing to form bonds, or overlapping orbitals), and no information is transferable or applicable to other molecules, even extremely similar ones.

an analogy would be like making a statue out of lego bricks vs 3D printing. the 3d printed statue is highly detailed and conforms exactly to the specifications, but it is solid and can't be taken apart. the lego statue is more crude and less realistic, but we can see and manipulate each constituent part that makes it up and learn how similar statues might be made based on the parts of this one.

that is the difference between exact and approximate in science.

>>8568685
sweet. are these introductory texts? or something to read after university physics?

The whole forumulation of Quantum Mechanics is basically just Linear Algebra

>>8568665
bookzz.org

>>8568741
Mathematics is exact. Physics isn't.