Module N (Nov 1)
- Compute partial derivatives
- Determine where multivariate functions are continuous
- Use a linear approximation to estimate the value of a function
- Solve separable ODEs
- Standard F2
Module S (Oct 18)
- Solve systems of two equations in two variables, even when coefficients are functions.
- Solve second order constant coefficient equations, including non-homogeneous ones.
- Standards C3,C5
- Model simple mechanical oscillators (e.g. spring-damper systems).
- Standard C6
- Find and classify the equillibria of autonomous ODES.
- Standard F4
Module F (Sep 25)
- Determine the intervals on which a polynomial is positive, negative, or zero.
- Use integration techniques like substitution, integration by parts, and partial fraction decomposition to compute indefinite integrals.
- Determine when a vector field is conservative.
- Find the potential function of a conservative vector field.
- Use variation of parameters to solve non-homogeneous ODEs when given the
solution to the corresponding homogeneous ODE
- Standard C5
Module C
- Describe Newton’s laws in terms of differential equations.
- Find all roots of a quadratic polynomial.
- Use Euler’s theorem to relate \(\sin(t)\), \(\cos(t)\), and \(e^t\) and to simplify complex exponentials.
- Use substitution to compute indefinite integrals.
- Use integration by parts to compute indefinite integrals.
- Solve systems of two linear equations in two variables.