# Calculus

- Elementary functions. Calculating limits, derivatives and integrals. Optimization problems
 Meta Thread / Thread Starter Last Post Replies Views Views: 5,095 Announcement: Follow us on social media and spread the word about PF! Jan16-12 Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:24 AM micromass 1 46,568 Since things are a bit quiet here, I thought I would throw out a puzzle I came up with several years ago, after... Feb17-06 03:09 PM NateTG 7 1,924 The definition of Y being connected in a topological space (X, tau) is that you can't find two non-empty, open and... May28-09 10:58 AM HallsofIvy 4 2,268 Hi all, i found this problem in a topology book, but it seems to be of an analysis flavour. I'm stumped. Show that... Dec15-08 01:56 PM Citan Uzuki 1 793 From Conway's Complex Analysis, page 17, 2.2.5: Suppose F \subseteq X is closed and connected. If a,b are in F and... Nov28-07 09:23 AM HallsofIvy 10 1,983 Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio... Jan27-10 02:24 PM daudaudaudau 8 3,272 I understand that the indefinite integral is like infinite definite integrals, but how come when we calculate the... Jan10-13 01:34 PM Whovian 12 2,247 Hellow! I want you note this similarity: \\ \int xdx=\frac{1}{2}x^2+C \\ \int x^2dx=\frac{1}{3}x^3+C \\ \sum... Dec30-13 09:32 PM pwsnafu 1 624 If exist a connection between the infinitesimal derivative and the discrete derivative $$d = \log(\Delta + 1)$$... Apr18-14 05:17 PM Jhenrique 6 426 Hey guys, I'm following a course on vector calculus and I'm having some trouble connecting things. Suppose we have a... Jan14-11 10:10 AM HallsofIvy 1 1,781 conponent(maximal connected set) must be closed, connected, open, disjoint. This is a fact. But why people still say... Nov4-10 08:41 AM micromass 3 734 Hi! Most of you know that the Frenet formulas written for the trihedron (\vec{T},\;\vec{N},\;\vec{B}) is ... Dec1-07 04:20 PM Abel Cavaşi 0 1,924 Hi I was wondering, one way that a conservative field can be found is if the line integral of any closed path is 0.... Jun8-11 09:45 PM micromass 1 853 It seems there are some problems on the test. I find that Curl F is not zero, that means the field is not exact. Am... Dec6-11 11:00 PM LCKurtz 1 871 This isn't homework. I'm reviewing calculus and basic physics after many years of neglect. I want to show that a... Jun15-13 12:53 AM inkliing 2 729 My calculus book states that a vector field is conservative if and only if the curl of the vector field is the zero... Dec6-09 06:24 AM HallsofIvy 2 2,061 Let f(x,y) = ( \frac{-y}{x^2 + y^2}, \frac{x}{x^2 + y^2}) with f : D \subset \mathbb{R}^2 \to \mathbb{R}^2 I... Dec24-11 07:13 AM Damidami 3 1,254 What does this mean ! ? Jul17-08 10:41 PM mathwonk 2 1,570 jjjj Jan31-08 09:44 AM HallsofIvy 1 3,878 Consider the heat equation in a radially symmetric sphere of radius unity: u_t = u_{rr}+{2 \over r}u_r \ for \ (r,t)... Aug27-09 02:44 PM tiny-tim 1 662 Use the chain rule to show that dz/dx = (cos(theta) * dz/dr) - (1/r * sin(theta) dz/dtheta) and dz/dy =... Sep8-13 03:59 AM CompuChip 1 659 I define a consistent family, F, to be a set of intervals such that if I_1 and I_2 are in F then I_1 and I_2... Feb28-08 08:11 PM Pere Callahan 6 1,777 Is there a formula that will calculate time when I know the following...? Initial velocity = 0 Final velocity =... Sep11-08 07:59 AM Photon713 3 1,708 If we parameterize the arc length of a vector valued function, say, r(s) and r(s) has constant curvature (not equal... Mar21-10 11:29 PM Tinyboss 1 1,121 Find a number "k" such that exist only one intersection between the curve exponential k^x e and the straight x·k. This... Nov17-13 05:54 PM PSarkar 5 567 My book (Saff&Snider) has the following theorem Suppose u(x,y) is a real-valued function defined in a domain D. If... Jun14-09 09:33 PM Tibarn 4 1,053 This is a question that came up in a conversation with my father who was a fighter pilot in ww2... we got to talking... Mar6-10 01:20 PM CompuChip 2 3,204 Hi everyone, I've been racking my brain about this problem, but can't seem to figure it out. It seems like it... Jun11-13 07:49 PM WannabeNewton 3 826 The first order KKT condition for constrained optimization requires that the gradient for the Lagrangian is equal to... Apr12-12 02:56 PM brydustin 4 1,015 Hi, I want to know the solution of the following equation. a = argmin_{a} \\ where x_i, y_i are column vectors... Apr15-11 05:29 AM jasonRF 2 2,891 Hi, I need help with this problem; minimize x^3, subject to K= x-Ωπ so would the solution be K-Ωπ=x Apr14-12 07:58 AM HallsofIvy 1 1,008 I'm trying to find the regular parallelepiped with sides parallel to the coordinate axis inscribed in the ellipsoid... Jul2-08 09:38 AM HallsofIvy 1 1,259 I have the analytical first and second derivatives of a (multidimensional) lagrangian ( l = f - λh). X is the vector... Jan21-12 05:04 PM brydustin 0 964 Construct a compact set of real numbers whose limit points form a countable set. Oct8-04 09:35 AM forget_f1 8 4,526 Suppose I'd like to construct a C^\infty generalization of a characteristic function, f(x): \mathbb R \to \mathbb R,... Oct31-11 02:32 PM Citan Uzuki 1 1,418 Today, I had the desire to construct a C^{\infty} approximation to a tent function. Specifically, for any positive... Mar13-06 11:39 PM Hurkyl 5 1,685 How do you construct Peano curves? All pictures I have seen suggest that it is iterative process, however, I don't... Sep22-08 05:50 PM Borek 0 812 Hello--- I am reading a paper on numerical methods which requires a 2D function to be converted to a 1D function. ... Mar2-10 09:43 AM nkinar 2 884 Can you prove that \mathbf{R} and \mathbf{R}-\mathbf{Q} have same cardinality? One way would be to say that... Sep19-08 06:25 AM morphism 3 1,826 This proof I think is related to our construction of R in class using equivalences classes of Cauchy sequences: Let... Nov3-11 04:01 PM autre 3 1,107 I was looking at the construction of the real number system. I know dedekind cuts can be used(completely worthless... Mar25-11 01:38 PM Liangpan 16 2,882