WeBWorK Homework For Exam 1 (final submission due 20 September at 11:59PM)
HW1 - Equations and solutions
HW2 - Existence and uniqueness and slope fields
HW3 - Solving first order equations
For Exam 2 (final submission due 18 October at 11:59PM)
HW4 - Higher order and linear independence and reduction of order
HW5 - Homogeneous linear ODEs with constant coefficients
HW6 - Cauchy-Euler and nonohomogeneous second order ODEs
HW7 - Laplace transform basics
HW8 - Solving IVPs with Laplace transform
For Exam 3 (final submission due 15 November at 11:59PM)
HW9 - Advanced Laplace transform properties
HW10 - Linear algebra basics
HW11 - Solving systems of linear differential equations
For Final Exam (final submission due 12 December at 11:59PM)
HW12 - Nonhomogeneous systems of differential equations
Quizzes For Exam 1
Quiz 1 [soln] (due 25 Aug at 11:59PM): Find the interval of existence and uniqueness for solutions to the problem $\left\{ \begin{array}{ll} (7t-2)y'+ty=\cos(t) \\ y(-5)=4 \end{array}\right.$.
Quiz 2 (due 27 Aug 28 Aug at 11:59PM): Consider the IVP $\left\{ \begin{array}{ll} y'=y+\sin(t) \\ y(0)=1.5 \end{array}\right.$. Use Euler's method (on a spreadsheet or by writing code) to numerically approximate the solution of this IVP with $h=0.5$ for $t \in [0,4]$. Your submission should include BOTH your spreadsheet (or code) and the plot as an image. The spreadsheet from the 26 August class is here.
Quiz 3 [soln] (due 1 Sep at 11:59PM): Consider the differential equation $y'=y^2+4y-21$. Find the critical points (aka equilibrium solutions) and classify each as asymptotically stable, semistable, or unstable.
Quiz 4 [soln] (due 3 Sep at 11:59PM): Solve the differential equation $y'=(t^3+1)(3y+7)$ using separation of variables.
Quiz 5 [soln] (due 5 Sep at 11:59PM): Solve the initial value problem $ty'+2y=\dfrac{\sin(t)}{t}, \quad y(\pi)=4$.
For Exam 2
Quiz 6 [soln] (due 24 Sept at 11:59PM): Find the general solution to
$$(\sin^2(t))y''-(2\sin(t)\cos(t))y'+(1+\cos^2(t))y=0,$$
given that $y_1(t)=\sin(t)$ is a known solution.
Quiz 7 [soln] (due 25 Sept at 11:59PM): Find the general solution of the ODE $y''-y'-6y=0$.
Quiz 8 [soln] (due 1 Oct at 11:59PM): Find the general solution of the ODE $y''+4y'+5y=0$.
Quiz 9 [soln] (due 3 Oct at 11:59PM): Find the general solution of the ODE $y''-3y'+2y=\dfrac{e^{3t}}{1+e^t}$.
Quiz 10 [soln] (due 6 Oct at 11:59PM): Compute the Laplace transform of the function $f(t)=t^2$ using the definition and integration by parts.
Quiz 11 [soln] (due 8 Oct at 11:59PM): Solve the following IVP using Laplace transform: $y'+2y=4, y(0)=1$.
For Exam 3
Quiz 12 [soln] (due 22 Oct at 11:59PM): Consider the function $\hat{f}(t)=t$ on $0 \leq t \lt 1$. Define a periodic function $f$ by $f(t+1)=\hat{f}(t)$ (notice this means that $f(t+T)=f(t)$ when $T=1$). Find the Laplace transform of $f$. note: this periodic function is called a "sawtooth wave"
Quiz 13 [soln] (due 29 Oct at 11:59PM): Find the eigenpairs of the matrix $\begin{bmatrix} 1&2 \\ 2&-2\end{bmatrix}$.
Quiz 14 [soln] (due 7 Nov at 11:59PM): Find the general solution of the system $\vec{x}'=\begin{bmatrix} 1&2 \\ 0&-1 \end{bmatrix}\vec{x}$.
For Final Exam
Quiz 15 (in-person quiz, no makeup): attend lab on 9 November in SH614 to receive this quiz