We first summarize what we have learned in the last semester to find the Taylor expansion of a given function. This has tremendous applications in all kinds of engineering. The single variable calculus ends here.

Then we move on to calculus in severable variables. The approach is similar to what we have done in the last semester: limit, derivative, optimization problem by using derivatives (Lagrange multipliers), integrals, then to ``Fundamental Theorem of Calculus.'' The formulas of FTC in two and three variables in the format of Green-Stokes and Divergence Theorems is technical to explain and learn. However, it all says that the net change of a vector function in the interior is exactly the total change (flux) on the boundary, when interpreted in a suitable sense.