Module C
- Describe Newton’s second law 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 and integration by parts to compute indefinite integrals.
- Solve systems of two linear equations in two variables.
- In addition, please read this article on mathematical intelligence.
Module F
- Determine the intervals on which a polynomial is positive, negative, or zero.
- Use substitution and integration by parts 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 first-order ODEs.
- Standard C2
Module S
- Solve systems of two equations with functional coefficients in two variables.
- Solve second order constant coefficient equations, including non-homogeneous ones.
- Standard C6
- Model basic mass-spring systems.
- Standard C7m
- Find and classify the equillibria of autonomous ODES.
- Standard F4
Module N
- Compute partial derivatives
- Determine where multivariate functions are continuous
- Use a linear approximation to estimate the value of a function
Module D
- Apply the method of partial fractions.
- https://prof.clontz.org/resources/calculus2/2/4/ (only 2.4.1)
- Compute improper integrals.
- https://prof.clontz.org/resources/calculus2/5/5/ (only 5.5.1)
- Model basic mass-spring systems.
- Standard C7m