Standards marked with “m” are modeling standards.
At the end of this course, you should be able to…
Solve and apply linear constant-coefficient ODEs.
- C1: Homogeneous first-order constant coefficient. Solve homogeneous linear constant coefficient first-order ODEs.
- C2: Non-homogeneous first-order constant coefficient. Solve nonhomogeneous linear constant coefficient first-order ODEs.
- C3m: Motion with linear drag. Model and analyze the vertical motion of an object with linear drag
- C4: Homogeneous second-order constant coefficient. Solve homogeneous linear constant coefficient second-order ODEs.
- C5: Initial value problems. Solve homogeneous linear constant coefficient second-order IVPs.
- C6: Non-homogeneous second-order constant coefficient. Solve nonhomogeneous linear constant coefficient second-order ODEs.
- C7m: Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP.
Solve and apply first-order ODEs.
- F1: Sketching trajectories. Sketch the trajectory of the solution of a first-order ODE given its slope field.
- F2: Separable IVPs. Find the solution to a separable IVP.
- F3m: Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag
- F4: Autonomous ODEs. Sketch and label the phase line of an autonomous ODE, and use it to determine the long-term behavior of solutions.
- F5: First-order linear IVPs. Find the solution to a first-order linear IVP.
- F6: Exact ODEs. Find the implicit general solution to a first-order exact ODE.
Solve and apply systems of ODEs.
- S1: Constant coefficient systems. Solve systems of first-order constant-coefficient IVPs.
- S2m: Coupled mass-spring systems. Model and analyze mechanical oscillators with a system of second-order IVPs.
- S3: Autonomous systems. Sketch and label the phase plane of an autonomous system of ODEs.
- S4m: Interacting populations. Model and analyze two interacting populations with an autonomous system of IVPs.
Use numerical approximation methods to analyze unsolvable IVPs.
- N1: Existence and uniqueness. Apply an existence and uniqueness theorem to a second-order linear IVP.
- N2: Euler’s method for IVP systems. Estimate the value of an IVP system solution using Euler’s method.
- N3m: Programming Euler’s method. Implement Euler’s method using technology.
Solve and apply ODEs that involve discontinuous functions or distributions.
- D1: Laplace transform. Compute the Laplace transform of a function from the definition.
- D2: Discontinuous IVPs. Use Laplace transforms to solve IVPs involving a step function or Dirac delta distribution.
- D3m: Non-smooth motion. Model and analyze motion involving instantaneous acceleration.
- D4m: Mass-spring impulse. Model and analyze motion of a mass-spring system involving an impulse.