Journal for Math 304 Spring 2010

May 8: I posted grades at the TAMU eLearning site. On the final exam, the median was 86, the mean was 81, and there were five scores of 100. Great job!
For the course averages, the median was 81 and the mean was 80.
May 7: The final exam was given, and solutions are available.
April 29: We reviewed for the final exam.
April 27: We discussed the diagonalization of matrices, the exponential of a matrix, and applications to systems of differential equations. The slides from class are available.
Thursday, April 29 is our last class meeting. During that class, we will review for the final exam.
The final exam is scheduled for Friday, May 7, from 12:30 to 14:30.
April 22: We discussed the application of eigenvalues and eigenvectors to the solution of systems of linear differential equations. The slides from class are available.
There is no assignment to turn in next time, but Exercise 2 on page 323 in Section 6.3 would be a good problem to do for practice.
April 20: We discussed eigenvalues and eigenvectors and the diagonalization of matrices. The slides from class are available.
The assignment for next time is Exercises 1(h), 3, and 11 on pages 310–311 in Section 6.1.
April 15: We discussed the Gram–Schmidt orthogonalization process and the related QR factorization.
The assignment for next time is Exercises 4 and 5 in Section 5.6 on page 282.
April 13: We discussed orthogonal sets, orthonormal sets, trigonometric polynomials, Fourier coefficients, and orthogonal matrices.
The assignment for next time is Exercises 2, 6, and 21(b)(i) in Section 5.5 on pages 271–272.
April 8: We discussed the notions of inner product and norm.
The assignment for next time is Exercises 3, 8, and 14 on pages 252–253 in Section 5.4.
April 6: I returned the graded exams in class. We discussed “solving” inconsistent linear systems by the method of least squares, and we did an example of finding a line that gives a best least-squares fit to a set of data.
The assignment for next time is Exercises 1c and 5a in Section 5.3 on pages 243–244.
April 3: I finished grading the second examination. The class average was 65, and the median was 67; there was one score of 100. Although on average the scores dropped in comparison to the first examination—reflecting the increased difficulty of the material—several students significantly improved their scores relative to the first examination, demonstrating that hard work pays off.
The grades are posted at the TAMU eLearning site. I will return the exams in class on Tuesday.
April 1: The second exam was given, and solutions are available.
March 30: We reviewed for the second exam.
March 25: We discussed orthogonal complements and the generalization of the rank–nullity theorem stating that N(A)^⊥=R(A^T).
The assignment for next time is Exercises 1d, 5, and 9 on page 233 in Section 5.2.
Reminder: The second exam takes place next week on Thursday, April 1, covering Sections 3.5 and 3.6, Chapter 4, and Sections 5.1 and 5.2.
March 23: We discussed scalar products and projections.
The assignment for next time is Exercises 6, 8c, and 13 on page 224 in Section 5.1.
Reminder: The second exam takes place next week on Thursday, April 1, covering Sections 3.5 and 3.6, Chapter 4, and Sections 5.1 and 5.2.
March 11: We continued discussing similar matrices. We looked at some examples of matrices that are or are not similar, and we saw that similar matrices must have equal determinants and equal traces.
The assignment for Spring Break is to have fun and to be safe.
March 9: We discussed similar matrices and the matrix representations of a linear transformation with respect to different bases.
The assignment for next time is Exercises 3 and 6 on page 205 in Section 4.3.
March 4: We discussed the representation of a linear transformation by a matrix.
The assignment for next time is Exercises 3c, 4b, 5b, and 13 on pages 197–198 in Section 4.2.
March 2: We discussed the notions of linear transformation, linear operator, kernel, image, and range.
The assignment for next time is Exercises 1c, 4, 6a, and 17c in Section 4.1 on pages 182–184.
February 26: I finished grading the first examination. The class average was 80, and the median was 82.5; there were three scores of 100. Good job!
The grades are posted at the TAMU eLearning site. I will return the exams in class on Tuesday.
February 25: We discussed the notions of row space, column space, rank, and nullity.
The assignment for next time is Exercises 8, 10, and 12 on pages 168–169 in Section 3.6.
February 23: We discussed the process of change of basis in a vector space.
The assignment for next time is Exercises 6 and 7 on page 161 in Section 3.5.
February 22: I was out of town last week due to a death in the family. The first exam was given on February 18, and solutions are available.
February 11: We discussed the notions of linear dependence, basis, and dimension.
The assignment for next time (not to hand in) is Exercises 6c and 11 on page 145 in Section 3.3 and Exercises 5 and 7 on page 150 in Section 3.4.
Reminder: The first examination is scheduled for Thursday, February 18 on sections 1.1–1.4, 2.1–2.2, and 3.1–3.4.
February 9: We looked at some more examples of subspaces, including the notion of the span of a set of vectors.
The assignment for next time is Exercises 3fg, 9ab, and 11 on pages 132–133 (Section 3.2).
February 8: I changed my Wednesday office hour for the rest of the semester to 13:00–14:00. My office hour on Tuesday and Thursday remains 15:00–16:00.
February 4: We discussed the definition of vector space and looked at some examples (and some non-examples). Then we discussed the notion of a subspace of a vector space. In particular, we looked at the important example of the nullspace of a matrix.
The assignment for next time is Exercise 10 on page 122 (Section 3.1) and Exercises 1ab and 4c on pages 131–132 (Section 3.2).
February 2: We looked at an example of computing a determinant both by cofactor expansion and by row and column operations. Then we worked in groups on Chapter Test A for Chapter 1 (page 88).
The assignment for next time (not to hand in) is to work on Chapter Test B for Chapter 1 (pages 88–89), problems 1–10. (Problems 11 and 12 concern partitioned matrices, a topic that we skipped.)
January 28: We skipped over Section 5 of Chapter 1 and discussed determinants and their properties.
The assignment for next time is Exercise 14 on page 59 (Section 1.3), Exercise 3g on page 97 (Section 2.1), and Exercise 1b on page 103 (Section 2.2).
January 26: We discussed elementary matrices and their applications to the algorithms for finding an inverse matrix (via Gaussian elimination) and an LU factorization of a matrix.
The assignment for next time is Exercises 3c, 4a, and 9a on pages 69–70 in Section 4 of Chapter 1.
January 21: We reviewed the method of Gaussian elimination by finding both a row echelon form and the reduced row echelon form for Exercise 5j on page 26. Then we discussed the algebra of matrices, including the operations of addition and multiplication and the notions of transpose and inverse. We observed from an example that matrix multiplication is not commutative.
The assignment for next time is Exercises 5i and 8 on pages 26–27 in Section 1.2 and Exercises 7, 10, and 13 on pages 58–59 in Section 1.3. In Exercise 13, notice that the notation a₁ means the first column of the matrix A; similarly, a₂ means the second column. (This notation is defined on page 31.)
January 19: We discussed the method of Gaussian elimination for solving systems of linear equations (Sections 1.1 and 1.2 in the textbook). Next time we will discuss matrix algebra (Section 1.3).
The assignment to hand in next time is Exercises 6d and 10 on page 12 in Section 1 of Chapter 1 and Exercises 3b and 5j on pages 25–26 of Section 2. Notice that three of these exercises have answers in the back of the book, so you need to explain how to get the answer.
January 15: Welcome to Math 304. I will be regularly updating this page with homework assignments, brief summaries of what we did in class, and other information.

Harold P. Boas