Syllabus
Slope field calculator
WeBWork Homework
For Exam 1 (final revisions due 14 September at 11:59PM)
HW1: Equations and solutions
HW2: Existence and uniqueness and slope fields
HW3: Solving first order equations
For Exam 2
HW4: Higher order and linear independence and reduction of order
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
For Exam 3
HW9: Advanced Laplace transform properties
HW10: Linear algebra basics
For Final Exam
HW11: Solving systems of linear differential equations
HW12: Nonhomogeneous systems of differential equations
Quizzes
Quiz 1 (due 20 Aug at 11:59PM) [soln]: do Example 1.1.9 parts b, c, d
Quiz 2 (due 27 Aug at 11:59PM) [soln]: Find the interval and existence and uniqueness for solutions to the problem
$\left\{ \begin{array}{ll}
(2x+1)y'+xy=\sin(x) \\
y(3)=-2 \end{array}\right.$
Quiz 3 (due 29 Aug) [soln]: Do the same analysis as we did in class to Example 1.2.13 to the differential equation $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \sqrt{17-x^2-y^2}$. That is, find the region $R$ where the solution is guaranteed to exist and be unique.
Quiz 4 (due 2 Sep3 Sep): Consider the differential equation $\left\{ \begin{array}{ll}
y'(t)=y(t)-\sin(t)\\
y(0)=0.5 \end{array}\right.$. It turns out that the solution to this differential equation is $y(t)=\dfrac{\sin(t)+\cos(t)}{2}$. Create a spreadsheet (as was done in class) to implement the Euler method for this differential equation for $t$ in $[0,4]$. Plot both the Euler method approximation with $h=0.1$ and the exact solution in the same plot. Your submission should include BOTH your spreadsheet AND the plot as an image.
You can find the spreadsheet I made implementting Euler's method in the Friday 30 August class here
Quiz 5 (due 23 Sep) [soln]: Given that $y_1(t)=\dfrac{1}{t}$ solves $2t^2y''+ty'-3y=0$ find the second independent solution using reduction of order.
Quiz 6 (due 1 Oct) [soln]: Compute the Laplace transform of the function $f(t)=t$ using the definition and integration by parts.
Quiz 7 (due 31 Oct) [soln]: Solve the iniital value problem $y''+2y'+2y=\delta(t-\pi), \quad y(0)=1, y'(0)=0$.
Exams
Exam 1
Exam 2
Exam 3
