Syllabus

Slope field calculator

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

HW6: Cauchy-Euler and nonhomogeneous second order ODEs

HW7: Laplace transform basics

HW8: Solving IVPs with Laplace transform

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

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.

Exam 1

Exam 2

Exam 3