| 2/13 | The first midterm will take place in class on 2/22. It will cover through Section 3.4. |
| 2/15 | We will have an optional review session on Tuesday, 2/20, 5th and 6th periods, in Hill 423 or 425 (check both rooms; they are adjoining). This will be an opportunity to discuss the review problems and any other topics. (Some brief answers are available here.) Students from Professor Speer's section C1 are welcome to attend, and students from section C3 are welcome to attend Professor Speer's review session on Sunday; details of time and place are on his web page, and the review problems for the two sections are identical in many respects. |
| 2/20 | Syllabus Update: We are now just about two classes behind the syllabus. |
| 3/29 | Syllabus Update: Still two classes behind the syllabus. |
| 4/3 | The second midterm will take place in class on 4/10. It will cover Sections 3.5 through 6.1 (inclusive). An optional review session is scheduled for Monday April 9, 11:30--12:50, in SEC 206. Again you may attend Professor Speer's review section, which will take place on Sunday April 8. Stay tuned to his web page for room and time details. Prof. Speer's students may also attend our review session. Click for review problems and some brief answers. |
| 4/17 | Syllabus Update: The plan for the rest of the semester is as follows. We have covered through Section 6.2 (and 10.1). On Thursday 4/19, we will cover part of 6.3 and 6.4. Then on Tuesday 4/24, we will jump to 6.7, the singular value decomposition, picking up only what is absolutely necessary from section 6.5 (positive definite matrices). The last class will contain an informal and brief introduction to linear transformations (chapter 7), and a bit of review. There will be a review session before the final exam. The final exam will take place on May 3, 12--3 p.m., in SEC 203. |
| 4/24 | An optional review session will be held on Tuesday, May 1 from 1:00-3:00 p.m. in SEC 205. The final exam will cover the entire course. Here are some review problems covering just the material since the second midterm, and some answers. |
| LAB: | #1 (PDF) | #2 (PDF) | #3 (PDF) | #4 (PDF) | #5 (PDF) | #6 (PDF) |
| DUE: | Jan. 30 | Feb. 20 | Mar. 22 (new date) | Mar. 22 | Apr. 26 | Apr. 26 |
| 1/18 | 1/23 | 1/25 | 1/30 | 2/1 | 2/6 | 2/8 | 2/13 | 2/15 | 2/20 | Midterm #1 |
| 2/27 | 3/1 | 3/6 | 3/8 | 3/20 | 3/22 | 3/27 | 3/29 | 4/3 | Midterm #2 |
| 4/17 | 4/19 |
(No quizzes were given on 1/25, 2/8, 2/20, 2/27, 3/8, 3/20, 4/3, 4/17, 4/19, but these might have been.)
| Section | Suggested Homework Problems |
| 1.1 | 1, 2, 4, 5, 6, 19, 20, 28, 29 |
| 1.2 | 1, 2, 4, 5, 12, 13, 14, 16, 17, 18, 19 |
| 2.1 | 1, 2, 3, 4, 9, 10, 15, 16, 17, 18 |
| 2.2 | 1, 2, 4, 5, 6, 12, 13, 14, 18, 19, 21, 22 |
| 2.3 | 1, 2, 3, 4, 10, 11, 16, 17, 18, 22, 23, 24 |
| 2.4 | 1, 2, 3, 4, 5, 6, 8, 12, 14, 18, 19, 20, 21, 25, 26, 28, 30 |
| 2.5 | 1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 17, 21, 22, 23, 24, 26, 27, 28, 34 |
| 2.6 | 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 21, 22 |
| 2.7 | 1, 2, 4, 6, 7, 10, 11, 16, 17, 19, 21 |
| 3.1 | 1, 2, 10, 12, 13, 15, 16, 19, 20, 22, 23, 26, 27, 28 |
| 3.2 | 1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 17, 18, 21, 23, 29, 30, 32, 33 |
| 3.3 | 1, 3, 4, 8, 12, 14, 15, |
| 3.4 | 1, 2, 3, 4, 7, 10, 12, 13, 15, 16, 17, 18, 21, 23, 25, 26, 29, 31, 33, 35, 36 |
| 3.5 | 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 17, 19, 21, 22, 23, 24, 25, 26 |
| 3.6 | 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 16, 17, 20, 21, 22, 23, 26, 27 |
| 4.1 | 3, 5, 7, 9, 13, 15, 17, 18 |
| 4.2 | 1, 3, 11, 12, 16, 17, 18, 19, 20, 21, 22 |
| 4.3 | 1, 2, 3, 5, 7, 17, 18, 19, 20, 21 |
| 4.4 | 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22 |
| 5.1 | 1, 2, 3, 4, 7, 10, 12, 13, 14, 15, 16, 17, 18, 23, 26, 27 |
| 5.2 | 1, 2, 3, 4, 5, 10, 11, 12, 13, 16, 19, 21, 22, 23 |
| 5.3 | 1, 2, 6, 8, 10, 13, 15 |
| 6.1 | 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 18, 24, 26, 27, 32 |
| 6.2 | 1, 3, 4, 8, 10, 15, 19, 20, 21, 22, 27, 35, 36 |
| 6.3 | 1, 4, 5 |
| 6.4 | 4, 5, 8, 11, 15, 16, 19, 20, 21 |
| 6.5 | 1, 2, 3, 6, 7, 8, 9, 11, 12, 15, 17, 19, 20, 21, 22, 25, 26 |
| 6.7 | 1, 2, 3, 4, 5, 7, 9, 10, 12, 13, 15 |
| 7.1 | 3, 7, 8, 10, 12, 21, 22, 23, 24 |
| 7.2 | 5, 6, 7, 8, 10, 11, 12, 15, 18, 29 |
| 7.3 | 1, 2, 5, 7 |
| 7.4 | 1, 2, 3, 5, 6, 7, 8, 9, 12, 13, 16, 21, 22 |
| 10.1 | 1, 2, 3, 7, 9, 12, 13 |
In section C3, computational labs using the MATLAB software package (version 5.3) are required. MATLAB is installed on PC's in all the Rutgers public computer labs (in ARC, Loree, College Avenue, Livingston). Students in the School of Engineering can also use MATLAB in the DSV Lab (Eng B-125/127) on Sun Ultra 10 workstations. You will need to bring a floppy disk with you to do the Lab assignments.
If you want to install MATLAB on your personal computer, you can purchase the Student Edition (for Windows 95/98, Linux or Macintosh) directly from MathWorks, Inc. The Student Edition includes some documentation and tutorials.
Although MATLAB is the preferred computational environment in this course, and is required for the Lab assignments, any graphing calculator will do some matrix algebra. More powerful ones (such as the TI-85 or TI-86) also do row reduction (LU decomposition) and eigenvalues/eigenvectors. You may find a calculator useful for some homework problems, but it is not required. Calculators (and crib sheets) will NOT be allowed on exams. There will be two midterm exams and a final exam;
six MATLAB assignments; textbook homework; and short unannounced
quizzes, given in class and based on the assigned homework problems.
These will combine as follows to determine your course grade:
| Midterm Exam #1 | 20% |
| Midterm Exam #2 | 20% |
| Homework and Quizzes | 8% |
| MATLAB Lab Assignments | 12% |
| Final Exam | 40% |
| Total | 100% |
There will also be two extra-credit optional Applied Linear Algebra projects (requiring some MATLAB), which can add to the above total, up to 3 percentage points each.
A PDF version of the syllabus and general information is available for print-out.
| Class date | Reading | Topics |
| 1/16 | 1.1, 1.2, 2.1 | Vectors, Lengths and Dot products, Vectors and Linear Equations |
| MATLAB Lab #1: Introduction to MATLAB (due 1/30) | ||
| 1/18 | 2.2, 2.3 | The Idea of Elimination, Elimination using Matrices |
| 1/23 | 2.4, 2.5 | Rules for Matrix Operations; Inverse Matrices |
| 1/25 | 2.6 | Elimination by a=LU Factorization |
| MATLAB Lab #2: a=LU Factorization | ||
| 1/30 | 2.7 | Transposes and Permutations, pa=LU Factorization |
| Extra-Credit Project #1: Graphs and Matrices | ||
| 2/1 | 3.1 | Spaces of Vectors |
| 2/6 | 3.2 | Nullspace of A |
| 2/8 | 3.3 | Rank; Echelon Matrices and Row Reduced Form |
| 2/13 | 3.4 | Complete Solution to ax=b |
| MATLAB Lab #3: Solving ax=b | ||
| 2/15 | 3.5 | Independence, Basis and Dimension |
| 2/20 | 3.6 | Dimensions of the Four Subspaces |
| 2/22 | Midterm Exam #1 (regular class time and place) | |
| 2/27 | 4.1 | Orthogonality of the Four Subspaces |
| 3/1 | 4.2, 4.3 | Projections; Least SQuares Approximate Solution to ax=b |
| MATLAB Lab #4: Vector Spaces and Approximate Solutions to ax=b | ||
| 3/6 | 4.4 | Orthogonal Bases, Gram-Schmidt Algorithm, a=QR Factorization |
| 3/8 | 5.1 | Determinant Function and its Properties |
| 3/20 | 5.2 | Permutations and Cofactors |
| 3/22 | 5.3 | Cramer's Rule, Inverses |
| MATLAB Lab #5: QR Factorization, Determinants and Eigenvalues | ||
| 3/27 | 6.1, 10.1 | Introduction to Eigenvalues and Eigenvectors; Review of Complex Numbers |
| 3/29 | 6.2 | Diagonalizing a Matrix |
| Extra-Credit Project #2 -- Graphs and Markov Processes | ||
| 4/3 | 6.3 | Applications to Differential Equations |
| 4/5 | 6.4 | Eigenvalues and Eigenvectors of Symmetric Matrices |
| MATLAB Lab #6: Symmetric Matrices, Positive Definite Matrices, Singular Value Decomposition | ||
| 4/10 | Midterm Exam #2 (regular class time and place) | |
| 4/12 | 6.5 | Positive Definite Matrices |
| 4/17 | 6.7 | Singular Value Decomposition (SVD) |
| 4/19 | 7.1, 7.2 | Linear Transformations and their Matrices |
| 4/24 | 7.3, 7.4 | Change of Basis; Dual Basis; Geometric meaning of SVD; ax=b by Pseudo-Inverse |
| 4/26 | Catch-up and Review | |
| Final exam: May 3, 12:00-3:00 p.m., in SEC 203 | ||