User contributions for Colors

24 April 2010

• 21:1921:19, 24 April 2010 diff hist +197‎ Definition talk:Stability (Differential Equations) ‎No edit summary

20 April 2010

• 18:4818:48, 20 April 2010 diff hist +475‎ N Definition:Lyapunov Function ‎ Created page with 'Let <math>x_0</math> be an equilibrium point of the system <math>x' = f(x)</math>. Then a function <math>V</math> is a '''Liapunov function''' of the system on an open set <math>…'
• 18:3818:38, 20 April 2010 diff hist +1,317‎ N Definition:Fundamental Matrix ‎ Created page with 'A matrix function <math>\Phi(t)</math> is a '''fundamental matrix''' of the system <math>x'=A(t)x</math> if it solves the matrix system <math>X'=A(t)X</math> and <math>\det \Phi(…'
• 18:0718:07, 20 April 2010 diff hist +78‎ N Definition:Non-Vanishing ‎ Created page with 'A function is said to be '''nonvanishing''' if it has no zeroes in its domain.'
• 04:1204:12, 20 April 2010 diff hist +103‎ User:Colors ‎No edit summary
• 04:1004:10, 20 April 2010 diff hist +356‎ N Bendixson-Dulac Theorem ‎ Created page with '== Theorem == If there exists a continuously differentiable function <math>\alpha(x,y)</math> on a simply connected domain, and :<math>\nabla \cdot (\alpha F) </math> is either…'
• 01:2101:21, 20 April 2010 diff hist +294‎ N Lyapunov's Stability Theorem ‎ Created page with '== Theorem == If <math>V</math> is a Liapunov function on an open set containing an equilibrium point <math>x_0</math>, then <math>x_0</math> is [[Stability (Differential Equ…'
• 01:0001:00, 20 April 2010 diff hist +1,471‎ N Floquet's Theorem ‎ Created page with '== Theorem == If: *<math>A(t)</math> is a continuous matrix function with period <math>\omega</math>, and *<math>\Phi(t)</math> is a fundamental matrix of …'

19 April 2010

• 18:5518:55, 19 April 2010 diff hist +6‎ m Putzer Algorithm ‎ woopserz
• 18:5318:53, 19 April 2010 diff hist +576‎ Putzer Algorithm ‎No edit summary
• 18:3018:30, 19 April 2010 diff hist +951‎ N Definition:Stability (Differential Equations) ‎ Created page with 'Often dynamical systems have as their solutions orbits, or periodic solutions; stability refers to how robust these solutions are with respect to small changes in their initial c…'
• 17:5517:55, 19 April 2010 diff hist +4‎ m Talk:Putzer Algorithm ‎No edit summary
• 17:5517:55, 19 April 2010 diff hist +393‎ Talk:Putzer Algorithm ‎No edit summary

17 April 2010

• 20:2120:21, 17 April 2010 diff hist +2,167‎ Properties of Matrix Exponential ‎No edit summary

15 April 2010

• 19:0419:04, 15 April 2010 diff hist +1,054‎ User:Colors ‎No edit summary
• 18:4218:42, 15 April 2010 diff hist +10‎ Properties of Matrix Exponential ‎No edit summary
• 18:4218:42, 15 April 2010 diff hist +740‎ N Properties of Matrix Exponential ‎ Created page with '<math>A</math> and <math>B</math> are constant matrices, <math>P</math> is a nonsingular matrix, and <math>t, s \in \mathbb{R}</math> === Derivative === <math>\frac{d}{dt} e^{At…'
• 18:2218:22, 15 April 2010 diff hist +117‎ m Putzer Algorithm ‎No edit summary
• 18:1718:17, 15 April 2010 diff hist +219‎ N Definition:Matrix Exponential ‎ Created page with 'The '''matrix exponential''', denoted <math>e^{At}</math> for the matrix <math>A</math>, is defined to be the unique solution to the IVP <math>X' = AX, \, \, X(0) = I,</math> whe…'
• 18:1318:13, 15 April 2010 diff hist +1,512‎ N Putzer Algorithm ‎ Created page with '== Method == Let <math>\lambda_1 , \lambda_2, \dots, \lambda_n</math> be the (not necessarily distinct) eigenvalues of the matrix <math>A</math>. Then: :<math>e^{At} = \sum_{k=…'
• 17:3017:30, 15 April 2010 diff hist +89‎ m Linearly Independent Solutions to 1st Order Systems ‎ →‎Proof
• 17:2717:27, 15 April 2010 diff hist +10‎ Inscribed Angle Theorem ‎ →‎Proof
• 17:2317:23, 15 April 2010 diff hist −1‎ Euler Polyhedron Formula ‎ →‎Proofs
• 17:2117:21, 15 April 2010 diff hist −10‎ m Inscribed Angle Theorem ‎ →‎Proof
• 17:2017:20, 15 April 2010 diff hist +223‎ Inscribed Angle Theorem ‎ →‎Proof

14 April 2010

• 20:2620:26, 14 April 2010 diff hist −13‎ Definition:Differential Equation ‎ →‎Autonomous system
• 20:0920:09, 14 April 2010 diff hist +873‎ N Euler Polyhedron Formula ‎ Created page with 'For any convex polyhedron with <math>V</math> vertices, <math>E</math> edges, and <math>F</math> faces, :<math>V - E + F = 2</math>. == Proofs == ===Induction on Vertices=== …'
• 19:4919:49, 14 April 2010 diff hist +150‎ N Maximum Modulus Principle ‎ Created page with 'Let <math>f</math> be a holomorphic function on a connected open subset of <math>\mathbb{C}</math>. Then <math>f</math> has no local maxima. {{stub}}'
• 18:3818:38, 14 April 2010 diff hist +693‎ Viète's Formulas ‎ →‎Proof
• 18:1818:18, 14 April 2010 diff hist +311‎ N Liouville's Theorem (Differential Equations) ‎ Created page with 'If <math> \Phi (t)</math> is a solution to the matrix differential equation <math>X' = A(t)X</math>, with <math>A(t)</math> continuous on the interval <math>I</math>, and <math>t…'
• 18:0418:04, 14 April 2010 diff hist +465‎ N Existence and Uniqueness Theorem for 1st Order IVPs ‎ Created page with 'If the <math>n \times n</math> matrix function <math>A(t)</math> and vector function <math>b(t)</math> are continuous on an interval <math>I</math>, then the Initial Value Proble…'
• 17:5117:51, 14 April 2010 diff hist +1,681‎ N Linearly Independent Solutions to 1st Order Systems ‎ Created page with 'The 1st-order homogeneous linear system of differential equations <math>x' = A(t) x</math>, expressed with the vectors <math>x', x: \mathbb{R} \to \mathbb{R}^n</math> and the mat…'
• 17:1117:11, 14 April 2010 diff hist +308‎ Definition:Differential Equation ‎No edit summary
• 17:0217:02, 14 April 2010 diff hist +6‎ Definition:Differential Equation ‎ →‎Ordinary Differential Equation
• 16:2816:28, 14 April 2010 diff hist +921‎ Inscribed Angle Theorem ‎ →‎Proof
• 05:3105:31, 14 April 2010 diff hist +10‎ Inscribed Angle Theorem ‎ →‎Proof
• 05:3105:31, 14 April 2010 diff hist +323‎ N Inscribed Angle Theorem ‎ Created page with 'An inscribed angle is equal to half the angle that subtends the same arc. In the figure below, <math>\angle BAC = \frac{1}{2} \angle BDC</math>. :[[Image:IncsribedAngle.PNG|300px…'
• 04:3404:34, 14 April 2010 diff hist +605‎ N Viète's Formulas ‎ Created page with '== Formulas == For a polynomial <math>P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0</math> with roots <math>z_1 , z_2, \dots, z_n</math> (not necessarily distinct), …'
• 02:0602:06, 14 April 2010 diff hist −38‎ Product of Sums ‎ →‎Corollary
• 01:1701:17, 14 April 2010 diff hist +84‎ Nm User:Colors ‎ Created page with 'I go by Colors here. I am a mathematical enthusiast interested in helping ProofWiki.'