Math 322 -- Mathematical Analysis for Engineers

	    - Practice problems for Exam 2 (some of these were assigned
	      as homework problems):

	      * 7.8 Matrix inverses # 1--10

	      * 7.7 Determinants # 7--15

	      * 7.4 Linear independence, rank, vector space
	        # 1--10, 17--25, 27, 30, 32, 33

	      * 1.1 First-order linear ODEs # 1--8

	      * 2.2 Homogeneous linear ODEs w/ const coeffs # 1--15

	      * 8.1 Eigenvalues and eigenvectors # 1--16

	      * 8.4 Diagonalization # 9--16

	      You are also responsible for knowing how to solve problems
	      similar to those I assigned as homework, even if they are
	      not in the text.  For example, you should know how to do
	      problems like this one.

	    - HW9 due Wed 3/25 Thu 3/26
	      8.1: #1, 2, 3, 4, 5, *10, *12
	      8.4: #9, 10, 11, 13, *14

	    - HW8 due Wed 3/11:
	      7.4: #4, 6, *7
	      Read 7.4, 7.5
	      In addition to bases for the row and column spaces, also
	      find a basis for the null space.

	      1.1: #17, 18
	      2.2: #1, 2, 3, 4, 5, 6, *14
	      For #14, find the solution with y(0) = y'(0) = 1.

	      Also write up this problem.

	    - HW7 due Wed 3/4 Fri 3/6:
	      7.4: #1, *3, 9, *17, 18, 19, 20, *27, 30, *31
	      (I may add a couple more problems to this set.)

	    - HW6 due Wed 2/25 (write-up due Mon 3/2)
	      7.7: #11, 12, *13, 14, *15
	      For 13-15, do it by both "cofactor expansions" (the
	      general definition I gave in class) AND by row reduction
	      to row echelon form.

	      7.4: #17, 18, 19, 20: I'll re-assign these for next
	      week.

	    - HW5 due Fri 2/20:
	      7.8: #1, 2, 3, 4, 5, 12, 15

	      (*) Problem:
	      Let A be the matrix
                                -1 - 2i   3 - 1i  -1 - 1i
                                 0 + 2i   2 - 3i   0 + 1i
                                 3 + 3i   0 + 0i   2 + 1i
              Find the inverse of A.

	      7.7: #7, 8
	      Read 7.7, 7.8

	      (I'm still planning to have a quiz on Friday.)
	      

	    - Some practice problems for exam 1:
              13.1: #3, 5, 11, 13, 15, 17, 19
              13.2: #7, 9, 11, 13, 17, 21, 23, 25, 27
	      13.5: #3, 5, 7, 17
	      13.6: #1, 9, 15
	      13.7: #15, 19, 21
	      7.1: #13, 15
	      7.2: #13, 15, 17
	      7.3: #9, 11, 13

	      (Some of the questions in 7.2 involve transposition, which
              we did not discuss in class but is part of your reading.
              It is very easy; just read the text.)

	      
	    - HW4 due Thu 2/12 at 5pm:
	      7.3: #4, 5*, 6*, 7, 10
	      For each problem, in addition to solving the linear system
	      represented by the augmented matrix, also do the
	      following:
 	       (i) Find the reduced row echlon form of the matrix.
	      (ii) Describe the geometry of the solution set -- is it
   	           a point, a line, or something else, and if so what?

	      7.2: read up to and including transposition
	      7.2: #11, 18

	    - HW3 due Wed 2/4:
	      7.1: #8, 9, 10, 11
	      7.3: #1, 3, *8, *13, *14
	      Problem: Solve the system of equations represented by the
	      following 2x3 augmented matrix
              1          -2 - 3i    3 - 2i
             -3 + 3i     16 + 3i   -4 + 14i
	      
	    - HW2 due Wed 1/28:
	      13.6: #3 6 7 8 11 12
	      13.7: #5 6 7 8 11 12 13 14 18

	    - HW1 due Wed 1/21:
	      13.1: #1, 2, 9, 12
	      13.2: #1, 2, 3, 5, 15, 21
	      13.5: #2, 9, 15

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