Math 3 for Nanobiologists

We begin this course with vector calculus; the study of integrals over curves and surfaces in 2 and 3 dimensions. In particular you will learn about the theorems of Green, Gauss, and Stokes.

Next you will study some more advanced concepts of linear algebra. We start with eigenvalues of a matrix, which provides better insight in what happens if you multiply a vector by that matrix. Next we consider the effects of orthogonality ("perpendicularness"), which amongst other things leads to regression (how best to draw a straight line through a set of experimental data). Finally we combine the two in the study of symmetric matrices which allow us to analyze quadratic forms and decompose a matrix in its singular value decompositions.

The course ends with the study of maxima and minima of functions of several variables (which uses the quadratic forms you just learned about), both local and global. In this topic you will also learn the technique of Lagrange multipliers.