Processing math: 75%
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
{(2x+1)y′+xy=sin(x)y(3)=−2
Quiz 3 (due 29 Aug) [soln]: Do the same analysis as we did in class to Example 1.2.13 to the differential equation dydx=√17−x2−y2. 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 {y′(t)=y(t)−sin(t)y(0)=0.5. It turns out that the solution to this differential equation is y(t)=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 y1(t)=1t solves 2t2y″ 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