advanced Definition and 507 Threads

Homework Statement My question is not specific to any particular problem but is rather of a conceptual nature. In my advanced calculus class this semester, the notation ds appears often, for line integrals, surface integrals, and arc length. In all honestly, I don't really understand what ds...

Lookin' for a good text on Advanced Calculus for self-study. Thanks.

As the title suggests, I'm looking for a good text on Advanced Calculus for self-study. Thanks.

Ok This is a long question so bear with me. BACKGROUND: I am designing a set of crush drums that counter rotate (similar to a rock crusher). One Drum is adjustable to increase/decrease distance between drums. Each drum is 170mm in diameter, 200mm long, made from 10mm thick steel. They are chain...

Hello everyone! I'm looking for an advanced quantum mechanics textbook. I've taken several undergrad quantum courses, but since starting my masters and taking grad courses in noncommutative geometry, functional analysis, and gauge theory to name a few I feel unsatisfied with the level of...

This might be a weird quest and in the wrong section but does anyone know of a list with errors and corrections for the book "Advanced Calculus" by Taylor & Mann 3rd ed? Thanks

Homework Statement If f is strictly decreasing and differentiable on R, then f '(x) ≤ 0 for all x. Homework Equations Mean value theorem The Attempt at a Solution if f is strictly decreasing, then for any a,b\inℝ such that a<b, f(b)<f(a) or f(b)-f(a)<0. By the MVT, there exists a...

Hi folks. I'm wondering who does a good job of explaining this limit, preferably with a good set of examples. It doesn't need to be too basic, but it'd be nice if it went through the phase space stuff a little (I get the impression that my grad prof didn't do a great job with some details based...

Homework Statement A particle of mass m rotates with a uniform speed on the inside of a bowl's parabolic frictionless surface in a horizontal circle of radius R=0.4 meters as shown below. At the position of the particle the surface makes an angle θ=20 degrees with the vertical. The angular...

Homework Statement A mass m is suspended by a light string from the ceiling of a moving car of mass M which is accelerating in the horizontal direction. The string makes an angle θ with the vertical as shown below. The acceleration of the car is: (A) mg/M (B) gsinø (C) g/tanø (D) mg/(m+M) (E)...

My school is offering a advanced mathematical methods classes next semester, taught by a supposedly world-renowned professor. Everyone to whom I've spoken, students and faculty alike, says he's an amazing teacher who gives you a unique education. However, here is the course description: My...

This question may be in the wrong section and quite irrelevant for many of you. Anyway, I need to buy a new calculator for my linear algebra course to deal with matrices and that stuff... which would you recommed I buy between the TI INSPIRE CX - CAS and the TI 89 TITANIUM? These are the ones my...

I intend for this post to serve as one place to get ideas (the vast majority of which are quite unoriginal with me). Naturally, no one solution method can possibly work for every problem. I would argue that such a solution method does not exist. However, the ideas that so many people have culled...

My main interest is usually physics, however I have become interested in the Fibonacci sequence. I looked at the sequence in detail and found a few interesting patterns. The main pattern was a relationship of the way that the digits of numbers compounded, the exact pattern was: 7,5,5,4,5,5...

Homework Statement A car with a flat front is accelerating in the horizontal direction so that an 80 kg person on the front face of the car stays in equilibrium. The coefficient of friction between the person and the surface of the car is .8. The resistance force by the air on the person is...

Hi, I'm 13 and wondering where I can learn this more advance Mathematics. Before you start thinking to your self "Well this little blighter must not pay attention at school!", I should probably explain why that statement would be invalid. You see, the Mathematical curriculum for my...

Such as topics in topology, complex analysis, etc.?

Homework Statement Secret Agent Jane Pond is testing out a new particle ray gun. She knows the particles in the ray have charge -2e and a mass of 50u. (u = atomic mass unit.) To determine the speed of the particles in the ray, Jane needs a region of uniform electric field. She takes...

I found the final answer posted online, but my work doesn't match up. v1 = 3t v2 = 5t1/2 - 6t Orthonormalized: v_1 = \sqrt{3}t is correct. v_2 = \frac{1}{\sqrt{61}}(5t^{1/2} - 6t) does not match. Furthermore, my part (b) is wrong, too. I know my methods are correct. I don't understand...

Homework Statement If ((a(n))+(a(n+1)))/2 converges to A, then a(n) converges to A. Either prove or disprove this conjecture. Homework Equations Normal convergence proof The Attempt at a Solution I will prove that ((a(n))+(a(n+1)))/2 converges to A such that for every...

class. I did a lecture last semester on financial mathematics and stochastic processes. Know of any cool topics that I could lecture on?

I'm trying to understand the basics of GTR. My textbook shows the worldline of an object freely falling into a Schwarzschild black hole in advanced Eddington-Finkelstein coordinates as neatly passing through a series of lightcones as it curves up right to left on the page toward the...

Last semester I took a combined course of Diffy Q and Linear Algebra. I feel I know the basics of LA and want to explore things a bit further. After talking to some professors at my school they told me that the next linear algebra class is a graduate class.. After looking at the course notes for...

Are you a software engineer using differential equations or more advanced math everyday to solve problems? I would like to hear about what you do--what projects do you work on? Do you consider that differential equations and advanced math skills are useful/in demand in the realm of software...

Homework Statement For arbitrary vector fields A and B show that; ∇ ^ (A^B) = (∇ . B)A - (∇.A)B + (B.∇)A - (A.∇)B Homework Equations where (A.∇)B = ((A.∇)Bx, (A.∇)By, (A.∇)Bz) and (A.∇)f = Ax δf/δx + Ay δf/δy + Az δf/δz = (Ax, Ay, Az)( δf/δx, δf/δy, δf/δz)f The Attempt at a...

Hello there, I was just reading some articles on Wikipedia.org and found an article on proton decay. I will quote a part of it: How would that be visualized? I've got a basic understanding of particle physics, but these concepts seem rather advanced, yet, I insist on wanting to understand...

I am planning to get into harvard physics division the requirements say that I should complete six advanced courses ,two mathematics and four physics courses .but i study in a technological university in India .But i am willing to do the courses outside .anyone with the similar problem and...

Hi, I am a sophomore physics major at the University of Minnesota. I have several options for technical electives and I will probably fill them up with math. Past the four-course math requirement, would it be better to take assorted courses such as PDEs or complex variables, or should I try...

Hello. I've been reading an interesting article by a pair of smart fellows... http://rmp.aps.org/pdf/RMP/v21/i3/p425_1 J. A. Wheeler, R. P. Feynman. "Classical Electrodynamics in Terms of Direct Interparticle Action". Reviews of Modern Physics. Volume 21. Number 3. 1949. I haven't...

Hey. I will be in approx. 1 year from now do a big mathematics project, that is going to be coupled with physics. I have already covered all the obvious choices for this project, such as harmonic motion and dampened harmonic motion with the derivation of the general solutions to the differential...

Homework Statement A security PIN code is four digits long. Each digit could have the value 0 to 9. if an office building needs 10 security PINs, express the number of codes in logarithmic form with base 10 The Attempt at a Solution y=4log(x-10) I don't know how to do the...

Hi i just wanted to know if anyone can help me located a system diagram with atleast 5+ forces acting on it? P.S. the diagram it self should be in rest position.

Hi, recently I've tried to find a good sintetic geometry book with both theory and exercises. Many people said well about this one https://www.amazon.com/dp/0486458059/?tag=pfamazon01-20 College Geometry. I've bought it and I've got so disappointed. I want a book that has exercises...

Homework Statement x= cosθ1p3(cosθ23)+cosθ1(cosθ2p2-a)-sinθ1p1 y= sinθ1p3(cosθ23)+sinθ1(cosθ2p2-a)+cosθ1p1 z= sinθ23p3-sinθ2p3 Homework Equations cosθ23 = cos(θ2 +θ3) sinθ23 = sin(θ2 +θ3) Finding θ1,θ2,θ3. Solve in terms of x,y,z,p Pls help to solve this algebra equation by eliminating the...

I'm looking for an advanced Calculus book that explains special (non-elementary) functions and their properties and applications (like Lambert W function, elliptic functions, error function, Ei and other special functions). I'd also like it to contain different methods of integration like...

On page 96, he defined \psi'(x')=S\psi(x), but it seems what he later derived for S only transforms the spinor part not the space-time coordinate of the 4-component wave function, then how is the space-time coordinate primed after acted by S? I'm pretty sure it's not a typo according to what he...

So far I've been working elementary math problems where the main focus is on creative ideas. I want to up my game but I find it hard to get past the first few chapters of more advanced books because they seem so daunting. For example, I wanted to get a foundation for complex analysis and learn...

Hello, I am currently trying to come up with an idea for a project for my advanced physics lab. I have thought to do supercooling/heating, superfluids, and perhaps a rail gun. I have access to a very nice high-speed camera, so I would hope to find an experiment that will utilize it (the rail...

Hello, We are all familiar with the formula that relates union of 2 mutually NOT exclusive events formula: P(A\cup B)=P(A)+P(B)-P(A\cap B) For 3 sets its easily derived using this formula. But I wanted to take this step further. I wanted to find a general formula, that represents...

Homework Statement A particle of mass m's velocity varies according to bx-n Find the position as a function of time, setting x = x0 at t=0 Homework Equations v(x) = bx-n possibly relevant: f(x) = -b2mnx-2n-1 The Attempt at a Solution The first part of the question asked me to...

Hello everyone, I'm really lost on where to start this problem; any thoughts? Thanks...

Hi all, I was just watching an old Feynman clip. In it, he describes areas where our observations are ahead of our theories (e.g. quasars) as well as areas where our theories are ahead of our observations (e.g. black holes). http://www.youtube.com/watch?v=6OrsaL97Epg&feature=related I...

Homework Statement Homework Equations The Attempt at a Solution Obviously I don't need a solution because it's right there. What I need to understand is what happened after the third equation sign and more importantly, how would I learn to solve these kinds of problems on my own. I looked at...

Homework Statement Let n=p^rm, where p is a prime not dividing an integer m>1. Prove that p does not divide C_n^{p^r}. Homework Equations There is a hint: Assume otherwise, cross multiply, and use Euclid's lemma. The Attempt at a Solution Although the author gives a hint, I...

I am a high school physics teacher in upstate NY. I am designing a new physics course and could use your help. I felt this forum was the best place for this post as the only other forum that may fit is the teacher sub forum, however, it appears to be little used and I would like input from...

Ok so I'm not sure if this is the right place to post this thread but I figured Earth/evolution? If not I can always move it to the biology section. Anyway I was speaking to a friend today who claimed that there have been periods of advanced human evolution in which the human mind over a...

Hello there, is there any computer software or programs out there that you can create various Faraday cages simulations

Hello, was wondering if anyone could please help me with the following questions as for math I have been given a substitute teacher who is of little help. Any help would be much appreciated, even if its just pointing me in the right direction Equation 1: Log (x-3) = 1 + Log 4 - Log x...

Hello I am currently studying Math B in high school and am having an extremely hard time with my current assessment. If anyone could please help me with the equations listed below it would be very much appreciated as my current Math teacher is on long service leave, and our substitute is...

I have seen a few recommendations on this forum that said a decent math preparation for a physics grad school should include advanced LA. What exactly would that include? What books would you suggest? Is this book one of them? https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20