I would add Tensor/Manifold/Lie theory though I guess the parts i'm thinking of are considered Differential Geometry. Seriously, allow me to make myself look ridiculous and say that Differential Geometry changed my life. They need to have it taught in undergrad more often.
Although this is only a qualitative answer I think the concept will more clearly motivate the math.
If we let the x-axis be space and the y-axis be time then velocity is a straight line in the spacetime plane.
For a given object let the line have a fixed length and to make it easier to...
I may be alone in this but I find that the more math I do the more "brainpower" I feel I have. It seems easier for me to pick up on things in general (not just in math but nonacademic areas too) after learning some math. A couple of days of hardcore proof-theorem study of a new topic also...
Sorry I didn't respond yesterday guys. I totally forgot I made a thread. I did well on the test and didn't fall asleep until 5 am... I think I went overboard with the caffeine. XD
What would you do? I don't think sleep is a viable option at this point except maybe a nap. I know I have to fix my sleep schedule but right now i'm worried about the current situation. Sorry if this isn't the right place for this type of question.
Sorry it took me so long to get back to you. Yeah I Swear. I mean we haven't done any E&M yet. As of last class we just derived Maxwell's Equations and I think we will be studying the actual physics now. When I said 1st course I meant 1st course in EM outside of Freshman year (sorry for the...
I'm just kind of curious how our school's E&M-I class compares to others because it seems like we are learning things at an advanced level (very fun though it can be intense).
We started the year off with Special Relativity then went into Vectors; nothing weird yet. Then instead of doing...
I've been thinking a lot about what Mathwonk said and now I'm confused even more. Now I don't know whether the Reals or the limit concept is more fundemental because I just realised I'd need to prove each using the other (at least at this stage).
So is this chapter in Apostol (the proof the OP stated is section 2.29) useless? It preceeds a discussion and proof of Bolzano's theorem so perhaps it makes sense in that context.
I'm not familiar with that book so I can't recommend it but I have Schaum's 3000 Problems in Calculus book and it is pretty good for problem solving practice. Most topics have over 100 questions ranging from simple calculation type to proof/theory based problems. Also for Physics Majors there...
Good luck. I'm in the same boat as you. Stewart is our required book in Uni and it's supposed to be written for laypeople but for some reason it confuses me with all the little boxes everywhere in all these different colors with distracting diagrams. Apostol on the other hand has the nice...
Oh Ok. I'll be more clear next time. I hope you enjoyed (or are still enjoying) the book. I'm working through it myself this summer to review and i'm previewing some of the Multivariable in Vol II as I go along.