2019 Spring - MAT 2680 - Reitz

"...how it differs from the rocks"

Page 2 of 4

How to enter ‘ (prime) in WeBWorK on your iPhone

April 11, 2019 / / 0 Comments

By default, the iPhone automatically converts straight quotes like this:  ‘
into smart quotes, like this ` .  You need to turn this functionality off in order to enter the prime (straight quote) symbol in WeBWorK.  The short version is:

To turn smart punctuation off, all you have to do is go to Settings > General > Keyboard, and then turn off the “Smart Punctuation” toggle.

More detailed instructions can be found here:

https://www.howtogeek.com/344310/how-to-turn-off-smart-punctuation-on-your-iphone-and-ipad/

 

Course Calendar updates

April 3, 2019 / / 0 Comments

Hi everyone,

Due to a number of factors (we one day behind the syllabus, Spring Break and Exam 3 timing, etc), I am making some minor changes to the class calendar – rearranging topics over the next few lectures.  The remaining material in Chapter 5 and Chapter 6 will be put off for a week or so, and tomorrow we will dive into Chapter 7 – Power Series (we’ll spend the next week or so working on this chapter).  See the most current schedule here.  Let me know if you have any questions.

Regards,
Prof. Reitz

 

 

 

WeBWorK 9: Tips for guessing solutions to nonhomogeneous equations

April 1, 2019 / / 0 Comments

Hi everyone,

As you work through WeBWorK #9, you may run into a few instances where it is not obvious what guess to make for the particular solution to the nonhomogeneous equation.  Here are two tips that might help:

 

What if the right side has both an exponential and a trig function?

If the right side of your differential equation has form similar to:  e^{ax} \cos(bx)

then your guess should have the form:  Ae^{ax} \sin(bx) + Be^{ax} \cos(bx)

 

What if the right side is a solution to the complementary equation (where the complementary equation has a repeated root)?

If your initial guess:  Ae^{ax} is a solution to the complementary equation, we adjust it by multiplying by x: Axe^{ax}.

If Axe^{ax} is *also* a solution to the complementary equation (due to a repeated root), adjust it by multiplying by x again:  Ax^2e^{ax}.

 

Let me know if you run into other weird things.  Questions are natural, and welcome!

Prof. Reitz

Assignments Week 9

March 25, 2019 / / 0 Comments

WeBWorK: Assignment  9-Nonhomogeneous  due Tuesday, 4/2, at midnight.
NOTE: Because of our exam on 4/2,  assignment 10-Trench-ReductionOfOrder will be due the following Tuesday, 4/9.

OpenLab:  OpenLab #2: Numerical Methods PROJECT is due Thursday, 4/4, by the start of class.

 

« Older posts Newer posts »

RSS Differential Equations on Math.Stackexchange

  • Finding integral curves to IVPs with accumulation functions
    I find it rather elegant that if you have a separable, first-order initial-value problem, $$\frac{dy}{dx} = \frac{f(x)}{g(y)}, \qquad y(a) = b$$ then you can implicitly solve it simply by creating two definite integrals (i.e. accumulations functions) based on the initial conditions: $$\int_{b}^{y} g(s)\,ds = \int_{a}^{x} f(t)\,dt$$ In particular, this means that any graphing software which […]
  • Separation of variables issue [duplicate]
    I'm currently trying to solve the following PDE - $$ \partial_{t}u(x,t) - \partial_{xx}u(x,t) = 0 \quad 0
  • Especial second order differential equation $y^{\prime\prime}y^{\prime}=f(x,y,y^{\prime}).$
    Can anyone provide examples of physical situations or mathematical problems where differential equations of the form $$y^{\prime}y^{\prime\prime}={A{y^{\prime}}^{5}+B{y^{\prime}}^{ 4}+C{y^{\prime}}^{3}+D{y^{\prime}}^{2}+Ey^{\prime}+F},$$ were $A,B,C,D,E$ are functions of $(x,y)$ only are useful ?
  • Will solutions of SDE with different initializations intersect at some point?
    Inspired by the result for ODE here, which shows that solutions to the same ODE with different initializations do not intersect, I am wondering if similar results also hold for SDE? Consider the SDE $$dX_t=f(X_t,t)dt+g(X_t,t)dB_t,$$ if both $f,g$ are Lipschitz with linear growth, then there must exists a unique strong solution for any independent initialization. […]
  • Jacobian matrix from mass action kinetic ODE network
    I have an ODE system consisting of >1000 equations for which I would like to obtain the Jacobian matrix. For simplicity, let's consider the following example: X1 --> X2 + X3 (on1) X1 + X2 --> X1 (off1) X3 --> X4 + X5 (on2) X4 + X5 --> X3 (off2) Assuming mass-action kinetics, the derivative […]
  • Particular integral for nth order differential equations with constant coefficients
    Say, I have an nth order differential equation with constant coefficients of the form, $$f(D)y=w(x)$$ Where $f(D)=\sum_{k=0}^{n}a_{k}D^{k}$ And $D^{k}$ denotes the $k$th derivative and $w$ is complete function in $x$. I need to show that solutions to such equations are of the form, $$y=p(x)+c(x)........(1)$$ Where $p(x)$ is particular integral and $c(x)$ is complementary function. I […]
  • Confluent-like Hypergeometric Function
    I'm trying to prove that one of the solutions of the equation $$xy''+y'+(c-x)y=0$$ is a Confluent Hypergeometric Function of the Second Kind times an exponential, that's what Mathematica says, I don't know how should I start
  • Intuition behind dampening as a rotation in the complex plane
    I'm currently building my intuition behind the meaning of the variables within the general second-order damped harmonic oscillator frequently taught in engineering: $$ \ddot{x} + 2\zeta\omega_n\dot{x} + \omega_n^2 x = 0 $$ Assuming an underdamped case, the eigenvalues are as follows: $$ \lambda = -\zeta w_n \pm w_n \sqrt{1 - \zeta^2} i $$ As such, […]
  • Differential equation Lagrange
    I have a problem solving this differential equation: $$ y = x(y')^2 - y' $$ Is anyone able to work out for me how to do this because I am at a loss? I would be very grateful for your help! Thanks.
  • Prove that two integrating factors define a solution.
    I've been toiling away at this proof problem from Chapter 2.4 ending exercises of Differential Equations 3rd ed by Shepley L. Ross, but to no avail. Show that if $\mu (x, y)$ and $v(x, y)$ are integrating factors of $$ M(x, y)\ dx + N(x, y)\ dy = 0 $$ such that $\mu (x, y) […]

© 2024 2019 Spring – MAT 2680 – Reitz

Theme by Anders Noren — Up ↑

The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.

Support

Help | Contact Us | Privacy Policy | Terms of Use | Credits

Accessibility

Our goal is to make the OpenLab accessible for all users.

Learn more about accessibility on the OpenLab

Copyright

Creative Commons

  • - Attribution
  • - NonCommercial
  • - ShareAlike
Creative Commons

top