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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 28th, 2019, 04:28 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 93 Wronskian application What is Wronskian used for? Here is the page of definition, but I need a simple example. https://en.m.wikipedia.org/wiki/Wronskian Last edited by skipjack; January 28th, 2019 at 09:26 PM. January 28th, 2019, 08:16 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. There is a section on that wiki page involving ODEs as an example. Thanks from idontknow January 29th, 2019, 02:08 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 93 Wronskian shows whether the solutions are linearly independent. If they are linearly independent the page says, $\displaystyle y_1 =xy_2$ . Why not $\displaystyle y_1=(ax+b)y_2$ ? January 29th, 2019, 07:36 PM #4 Senior Member   Joined: Sep 2016 From: USA Posts: 647 Thanks: 412 Math Focus: Dynamical systems, analytic function theory, numerics The only application I know of is an easy proof that some collection of functions are linearly independent. Namely, if $W(f_1,\dots,f_n) \neq 0$ on some domain, $D$, then the set of functions $\{f_1,\dots,f_n\}$ restricted to $D$ form a linearly independent set. Linear independence does not mean $y_1 = xy_2$ nor does it mean $y_1 = (ax + b)y_2$. I don't know where you got either of these formulas. The definition says that if $V$ is a (finite-dimensional) vector space, then $\{v_1,\dots,v_n\} \subset V$ are linearly independent if whenever $a_1v_1 + \dots + a_nv_n = 0$ you must have $a_j = 0$ for every $j$. In English, if a linear combination of linearly independent vectors is zero, then every coefficient is zero. In the case of the Wronskian, the vector space is the space of functions which are $n$ times differentiable so that this determinant makes sense. This is a standard example of a vector space which you should have seen in a first linear algebra class. Tags application, wronskian Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Survivornic Calculus 0 October 14th, 2012 09:20 AM triplekite Applied Math 2 October 11th, 2012 06:48 PM rkj66 Applied Math 0 February 6th, 2012 10:44 AM roniy Differential Equations 1 February 18th, 2010 10:04 PM bjalongi Linear Algebra 0 February 12th, 2008 07:47 PM

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