Does cos(1/z) Verify Picard's Big Theorem Near z=0? - Physics …
2013年10月6日 · First, better define what you mean by Picard's Theorem. He has two, the little one and the big one. Little: Every entire function that's not a polynomial has an essential …
Understanding the Cauchy Problem with the Picard Theorem
2007年4月12日 · Picard's theorem is what you probably guessed: Given any point in the plane, (x 0, y 0), and a function f(x,y), continuous on some neighborhood of (x 0, y 0) and Lipschitz in y …
Picard's existence theorem for DE - Physics Forums
2009年2月21日 · Homework Statement I was talking with my maths lecturer about how he knew certain special differential equations such as y'' = y has only y = e^x + e^-x...
Picards Existence and Uniqueness theorem doesn't prove anything
2011年6月20日 · As far as I can understand it, Picard's Existence and Uniqueness of ODEs theorem relies on the fact that a the given function f(x,t) in the initial value problem dx/dt = …
What does a function takes on mean? - Physics Forums
2013年11月8日 · Hey! I'm currently learning Picard's theorem, but I don't quite understand it because of difficult words.. In the text, it uses the term "takes on", ie "If f(z) is analytic and has …
The Pantheon of Derivatives – Part V - Physics Forums
2017年3月25日 · Great Picard’s Theorem [28] Let ##f## be a holomorphic function with an essential singularity at a point ##z_0##, then on any punctured neighborhood of ##z_0##, …
Picard's Iteration: Solving dy/dx=y^2 - Physics Forums
2005年8月22日 · The initial value problem has a solution if and only if that integral equation has a solution. The integral equation can be thought of as a "fixed value" problem and, since …
Differential Equations: Picard's Existence Theorem - Physics Forums
2008年3月30日 · Differential Equations: Picard's Existence Theorem Thread starter mattst88; Start date Mar 30, 2008; Tags ...
How is Euler's Identity proven using differential equations?
2021年4月21日 · Then, since these two functions satisfy the same differential equation with the same initial condition, by the uniqueness of the solutions (Picard's theorem) they must be the …
Simple existence/uniqueness proof for Newton's 2nd? - Physics …
2010年6月6日 · Is there a simple proof of the existence and uniqueness of a solution of x''(t)=f(x'(t),x(t),t), where f is an appropriately "nice" function?