Guidelines for Exam 2 preparation

To be successful on Exam 2, you should

• understand the definition of improper integral, in situations where the interval of intergation is infinite, or where interval is finite but the integrand is unbounded at an endpoint.
• be able to evaluate improper integrals in elementary cases.
• understand the ideas behind the trapezoidal rule, midpoint rule, and Simpson's rule for approximating definite integrals.
• be able to calculate by hand" approximations using the rules above.
• be able to set up integrals for the length of curves given in the form y=f(x), x=g(y), or by parametric equations x=x(t), y=y(t).
• understand the meaning of "centroid" and "center of gravity" of a planar region, and be able to use geometric considerations and/or symmetry to draw conclusions about the location of such points.
• be able to set up integrals for the coordinates of the centroid of a planar region.
• understand Pappus' Theorem and be able to apply it to find the centroid of a planar region, or the volume of solid of revolution.
• understand the meaning of "ordinary differential equation."
• understand what it means to be a solution of a differential equation.
• know the difference between "general solution" and "particular solution" of a first order ODE.
• be able to recognize autonomous and separable first order ODEs.
• understand what is meant by "slope field" or "direction field," and how it relates to an ODE and its solutions.
• be able to find equilibrium solutions of autonomous equations, and sketch "phase diagrams" on the dependent variable axis.
• be able to find the general solution of first order autonomous or separable ODEs.
• be able to find particular solutions of first order autonomous or separable ODEs with given initial conditions.
• be able to set up first order ODEs to model physical situations such as mixing, Newton's Law of Cooling, growth models, radioactive decay.