https://dananne.org/dw/ 2026-05-06T06:12:17+00:00 https://dananne.org/dw/ https://dananne.org/dw/lib/tpl/codowik/images/favicon.ico text/html 2014-08-26T10:14:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-1&rev=1409073280&do=diff Mathematics 255 - Fall 2014 Homework Section 1.2: 1, 2, 3, 5, 6 text/html 2014-08-28T14:54:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-2&rev=1409262868&do=diff Mathematics 255 - Fall 2014 Homework Section 1.3: 1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14 Section 1.4: 1, 2, 3, 5 text/html 2014-09-02T07:17:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-3&rev=1409667467&do=diff Mathematics 255 - Fall 2014 Homework Section 2.1: 1, 2, 3, 4, 5, 6, 7, 9 text/html 2014-09-04T08:32:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-4&rev=1409844758&do=diff Mathematics 255 - Fall 2014 Homework Section 2.2: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 text/html 2014-09-07T06:50:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-5&rev=1410097806&do=diff Mathematics 255 - Fall 2014 Homework Section 2.3: 1, 2, 3, 4, 5, 6 Section 2.4: 1, 2, 3, 4, 5, 6 text/html 2014-09-09T06:41:23+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-6&rev=1410270083&do=diff Mathematics 255 - Fall 2014 Homework Section 2.6: 1, 2, 3, 4, 5, 6 text/html 2014-09-11T06:07:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-7&rev=1410440867&do=diff Mathematics 255 - Fall 2014 Homework Section 2.6: 7, 8, 9, 10 text/html 2014-09-17T07:13:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-8&rev=1410963186&do=diff Mathematics 255 - Fall 2014 Homework Section 3.1:1, 2 Also: Suppose the population of a certain country was 100 million in 2005 and 110 million in 2010. Assuming the exponential growth model, predict the population for the country in 2015. Also, find the year in which the population will have doubled from its size in 2005. text/html 2014-09-23T15:41:08+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-9&rev=1411512068&do=diff Mathematics 255 - Fall 2014 Homework Section 3.1: 3, 4 Section 3.2: 1, 2 Also: * A bone fossil is determined to have 5% of its original carbon-14 remaining. How old is the fossil? * Plutonium-239, the fuel for nuclear reactors, has a half-life of 24,000 years. How many years will it take before there is only 10% left? How many years until only 5% remains? text/html 2014-09-18T07:13:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-10&rev=1411049585&do=diff Mathematics 255 - Fall 2014 Homework Section 3.3: 1, 3, 7, 15 You do not need to identify the model. text/html 2014-09-21T09:07:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-11&rev=1411315678&do=diff Mathematics 255 - Fall 2014 Homework Section 4.2: 1, 2, 3, 4, 5 text/html 2014-09-30T09:08:59+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-13&rev=1412093339&do=diff Mathematics 255 - Fall 2014 Homework Section 4.4.1: 1, 2, 3, 4, 5, 6, 7, 8 Also: * Suppose $p$ and $q$ are continuous functions on an open interval $J$, and that $y_1$ and $y_2$ are both solutions of $y'' + p(t)y' + q(t)y = 0$ on $J$. Moreover, suppose that for some $t_0$ in $J$, $y_1(t_0) = 0$ and $y_2(t_0) = 0$. Show that $y_1$ and $y_2$$J$$p$$q$$J$$y_1$$y_2$$y'' + p(t)y' + q(t)y = 0$$J$$y_1$$y_2$$t_0$$J$$y_1$$y_2$$J$ text/html 2014-10-02T05:40:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-14&rev=1412253630&do=diff Mathematics 255 - Fall 2014 Homework Section 4.4.2: 1, 2, 3, 4, 7, 8, 9, 10, 11, 12 text/html 2014-10-06T08:53:03+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-15&rev=1412610783&do=diff Mathematics 255 - Fall 2014 Homework Section 4.4.3: 1, 2, 3, 4, 5, 6, 7, 8 Also: Given functions $f_1$ and $f_2$, show that $W[f_1 + f_2, f_1 - f_2](t) = -2W[f_1, f_2](t)$. text/html 2014-10-07T06:15:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-16&rev=1412687725&do=diff Mathematics 255 - Fall 2014 Homework Section 4.5.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 text/html 2014-10-09T05:56:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-17&rev=1412859405&do=diff Mathematics 255 - Fall 2014 Homework Section 4.5.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31 text/html 2014-10-21T06:08:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-18&rev=1413896900&do=diff Mathematics 255 - Fall 2014 Homework Section 4.5.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 26, 27, 29 Find the general solutions, using variation of parameters and the results we obtained in class. Also: Find the particular solution of $y'' + 4y' + 4y = t^{\frac{5}{2}}e^{-2t}$ satisfying $y(0) = 0$$y'(0) = 0$$y(t) = \frac{4}{63}t^{\frac{9}{2}}e^{-2t}$ text/html 2014-10-16T09:43:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-19&rev=1413477780&do=diff Mathematics 255 - Fall 2014 Homework Section 4.6: 1, 5, 7, 8, 9, 10 text/html 2014-10-19T09:40:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-20&rev=1413736838&do=diff Mathematics 255 - Fall 2014 Homework Section 5.1.1: 1, 3, 4 Section 5.1.2: 1, 2, 3 text/html 2014-10-26T12:13:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-21&rev=1414350796&do=diff Mathematics 255 - Fall 2014 Homework Section 5.2.1: 1, 3 Section 5.2.2: 1 Also: Let $A$ be the amplitude of the particular solution of $m\frac{d^2y}{dt^2} + \gamma\frac{dy}{dt} + ky = f_0\cos(\omega t)$ as found in class. Show that $A$ has a maximum value when $\omega^2 = \omega_0^2 - \frac{1}{2}\left(\frac{\gamma}{m}\right)^2$. text/html 2014-10-30T06:28:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-23&rev=1414675686&do=diff Consider the first-order linear system $\dfrac{d\mathbf{x}}{dt} = \begin{bmatrix}-3 & -2 & \phantom{-}3\\ \phantom{-}1 & \phantom{-}0 & -3\\ \phantom{-}1 & -2 & -1\end{bmatrix}\mathbf{x}$. * Show that $\mathbf{x}^{(1)}(t) = \begin{bmatrix}e^{-2t}\\ e^{-2t}\\ e^{-2t}\end{bmatrix}$, $\mathbf{x}^{(2)}(t) = \begin{bmatrix}\phantom{-}e^{2t}\\ -e^{2t}\\ \phantom{-}e^{2t}\end{bmatrix}$, and $\mathbf{x}^{(3)}(t) = \begin{bmatrix}-e^{-4t}\\ \phantom{-}e^{-4t}\\ \phantom{-}e^{-4t}\end{bmatrix}$ are lin… text/html 2014-11-03T06:46:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-24&rev=1415025965&do=diff Mathematics 255 - Fall 2014 Homework Section 7.4.1: 1, 3, 5, 7, 9, 11, 13, 15 You do not need to sketch the phase portrait. text/html 2014-11-03T17:31:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-25&rev=1415064692&do=diff Mathematics 255 - Fall 2014 Homework Section 7.4.2: 1, 3, 5, 7, 9 You do not need to sketch the phase portrait. text/html 2014-11-08T07:50:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-26&rev=1415461825&do=diff Mathematics 255 - Fall 2014 Homework Section 7.4.3: 1, 3, 5, 7, 9, 11, 13 You do not need to sketch the phase portrait. text/html 2014-11-11T06:53:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-27&rev=1415717624&do=diff Mathematics 255 - Fall 2014 Homework Section 9.2: 1, 3, 5, 7, 9 text/html 2014-11-14T08:58:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-28&rev=1415984285&do=diff Mathematics 255 - Fall 2014 Homework Section 9.2: 11, 13, 15, 17 Also: * The equation $y'' - 2ty' + \lambda y = 0$, where $\lambda$ is a constant, is known as Hermite's equation. * Find the first five nonzero terms of two linearly independent series solutions. What is the interval of convergence?$n$$\lambda = 2n$$\lambda = 8$$(1 - t^2)y'' - 2ty' + \alpha^2 y = 0$$\alpha$$n$$\alpha = n$$\alpha = 5$ text/html 2014-11-16T08:46:23+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-29&rev=1416156383&do=diff Mathematics 255 - Fall 2014 Homework Section 8.1: 1, 3, 5 text/html 2014-11-23T12:20:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-30&rev=1416774057&do=diff Mathematics 255 - Fall 2014 Homework Section 8.1: 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 You should be able to do these without Appendix C. Also, do not use convolutions for 25, 27, and 29. text/html 2014-12-02T06:11:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-31&rev=1417529462&do=diff Mathematics 255 - Fall 2014 Homework Section 8.2: 9, 11, 13, 15, 23, 25, 27 Section 8.3.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 You should be able to do the exercises from 8.2 without Appendix C. text/html 2014-12-02T06:10:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-32&rev=1417529445&do=diff Mathematics 255 - Fall 2014 Homework Section 8.2: 1, 3, 5, 7, 17, 19, 21, 29 Section 8.3.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 You should be able to do the exercises from 8.2 without Appendix C. text/html 2014-12-05T06:41:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-255:m255-f14-hw:hw-33&rev=1417790495&do=diff Mathematics 255 - Fall 2014 Homework Section 8.3.3: 1, 3, 5, 7, 11