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.