Syllabus
Slope field calculator
WeBWorK
WeBWorK Homework
For Exam 1 (final submission due 21 September at 11:59PM)
HW1 - Equations and Solutions
HW2 - Existence and uniqueness and slope fields
HW3 - Solving first order equations
HW4 - Higher order and linear independence and reduction of order
HW5 - Homogeneous linear ODEs with constant coefficients (only finding general solutions on exam 1)
For Exam 2 (final submission due 26 October at 11:59PM)
HW5 - Homogeneous linear ODEs with constant coefficients
HW6 - Cauchy-Euler and nonhomogeneous second order ODEs
HW7 - Laplace transform basics
HW8 - Solving IVPs with Laplace transform
HW9 - Advanced Laplace transform properties
For Exam 3 (final submission due 30 November at 11:59PM)
HW9 - Advanced Laplace transform properties
HW10 - Linear algebra basics
HW11 - Solving systems of linear differential equations
HW12 - Nonhomogeneous systems of differential equations
Quizzes
For Exam 1
Quiz 1 (due 27 Aug at 11:59 PM) [soln]: Find the interval of existence and uniqueness for solutions to the problem $\left\{ \begin{array}{ll}
(5t+2)y'+ty=\cos(t) \\
y(-1)=5 \end{array}\right.$
Quiz 2 (due 29 Aug): Consider the differential equation $\left\{ \begin{array}{ll}
y'=y-\cos(t) \\
y(0)=0.5 \end{array}\right.$. Create a spreadsheet as was done in the class to numerically approximate the solution with Euler's method with $h=0.5$ for $t$ in $[0,4]$. Your submission should include BOTH your spreadsheet and the plot as an image.
Spreadsheet from the 28 August class is here
Quiz 3 (due 3 Sep) [soln]: Solve the separable initial value problem $y'=e^{-y}(5t-2), y(3)=7$.
Quiz 4 (due 5 Sep) [soln]: Find the general solution of $y'+3t^2y=6t^2$.
Quiz 5 (due 10 Sep) [soln]: First show that the functions $y_1(x)=\sin(x)$ and $y_2(x)=\cos(x)$ solve the differential equation $y''=-y$. Then show that $\{y_1,y_2\}$ forms a linearly independent set of solutions.
For Exam 2
Quiz 6 (due 12 Sep) [soln]: Find the general solution of the ODE $y''-6y'+8y=0$.
Quiz 7 (due 26 Sep) [soln]: Find the general solution of the ODE $y''-y=2t^2-t-3$.
Quiz 8 (due 29 Sep) [soln]: Compute the Laplace transform of the function $f(t)=t$ using the definition and integration by parts.
Quiz 9 (due 1 Oct) [soln]: Find the inverse Laplace transform of $\dfrac{s+1}{s^2+2s}$.
Quiz 10 (due 3 Oct) [soln]: In class, we showed that $\mathscr{L}\{y'\}(s)=s\mathscr{L}\{y\}(s)-y(0)$. In this quiz, use integration by parts to show that $\mathscr{L}\{y''\}(s)=s^2\mathscr{L}\{y\}(s)-sy(0)-y'(0)$.
Quiz 11 (due 8 Oct) [soln]: Use the Laplace transform method to solve the nonohomogeneous differential equation $y''+4y=2e^{-t}$ equipped with data $y(0)=1$ and $y'(0)=0$.
For Exam 3
Quiz 12 (due 20 Oct): in-person lab quiz during 16 October class (no makeup) -- hand in to me in-person or in my mailbox on Smith Hall 5th floor in room next to the math+physics dept admisitrative assistant's office
Quiz 13 (due 29 Oct) [soln]: Solve the initial value problem $y''+2y'+2y=\delta(t-\pi), \quad y(0)=1, y'(0)=0$.
Quiz 14 (due 7 Nov) [soln]: Find the general solution of the system of differential equations $\vec{x}'=\begin{bmatrix} 1&1 \\ 0 &-1 \end{bmatrix}\vec{x}$.
Quiz 15 (due 12 Nov): Find the general solution of the system of differential equations $\vec{x}'=\begin{bmatrix} 1&-1 \\ 1&1 \end{bmatrix}\vec{x}$.
