Summary: Math 320 (spring 2011) About the second midterm
Here is a list of the topics which we have covered in class since the previous
midterm. You should also see also the assigned homework problems on the course
Linear algebra The definition of linear independence. Know the definition
(see page 248). "Know the definition" means "know the definition," i.e., if you are
asked for the definition, then you should be able to state it. Know how to use the
definition (in combination with row reduction) to prove a given list of vectors is
independent or not (as in examples 5 and 6 on pages 249250.)
Linear algebra subspaces. Know the definition: in this course we have adopted
theorem 1 on page 241 as the definition. Be able to prove/disprove that a given
set S is a linear subspace of Rn
. Be able to find a basis for the solution space of a
given set of linear equations (see the algorithm and example on pages 258/259).
You should also know the definition of a basis, and you should know the defi-
nition of when a set of vectors spans a given subspace.
The above topics are covered in the book in §§4.24.4.
Differential equations first order. You should know how to solve separable
equations (y = f(x)g(y), see §1.4) and linear equations (y + P(x)y = Q(x), see
§1.5). None of this is new, as you have already seen this material in math 222.