MATH 461 Linear Algebra for Scientists and Engineers
Exam Schedule
- First Exam:
- Wednesday, 29 September
- Second Exam:
- Friday, 22 October
- Third Exam:
- Friday, 3 December
- Final Exam:
- Wednesday, 15 December 2004, 8 - 10.
Grading Policy
Grades will be based on three hour exams counting
100 points each, homework and quizzes worth 100 points, MATLAB assignments
worth 100 points, and a final examination that is worth 200 points.
Class Schedule
The class meets according to the following schedule:
- Monday, Wednesday, and Friday, 11:00-11:50
- Math Building B0421.
Topics
- TOPICS
- Systems of Linear Equations
- Gaussian elimination
- Echelon forms
- Existence and uniqueness of solutions
- Homogeneous systems
- Matrices
- Addition, scalar multiplication, multiplication of matrices
- Elementary matrices and inversion
- LU decomposition
- Systems of linear equations as matrix equations
- Determinants and their properties
- Cramer's rule
- Vector Spaces
- Subspaces and spanning sets
- Linear independence
- Basis and dimension
- Row and column spaces of a matrix
- Rank of a matrix
- Null space of a matrix
- Linear Transformations
- Kernel and range
- Matrix representation
- Change of basis and similarity of matrices
- Scalar Products and Orthogonality
- Cauchy-Schwarz and triangle inequalities
- Length and angles
- Pythagorean theorem
- Orthonormal sets
- Orthogonal complements of the null space and column space
- Orthogonal projection
- Least squares problems
- Orthogonal matrices
- Gram-Schmidt process and QR factorization
- Eigenvalues
- Complex eigenvalues
- Diagonalization of matrices
- Spectral theorem for symmetric (*hermitian) matrices
- Positive definite matrices
- Singular Value Decomposition
Topics in Lay
We wil cover parts of Chapters 1-7
(Sections 2.4-2.9, 4.8,5.6,5.7,5.8,7.4,7.5 optional)
of Lay's book.
Math 461: Provisional Schedule
Sections are from Linear Algebra and its
Applications, 3rd edition by Lay.
| WEEK | Monday | Wednesday | Friday |
|---|
| Aug 30-Sep 3 | 1.1 | 1.2 | 1.3(Q1) |
| Sep 6 - Sep 10 | Labor Day Holiday | 1.4-5 | 1.7 |
| Sep 13 - Sep 17 | 1.8 | 1.9 | 1.10(Q2) |
| Sep 20 - Sep 24 | 2.1 | 2.2 | 2.3(Q3) |
| Sep 27 - Oct 1 | Review | EXAM #1 | 3.1-2 |
| Oct 4 - Oct 8 | 3.2-3 | 4.1 | 4.2(Q4) |
| Oct 11 - Oct 15 | 4.3 | 4.4 | 4.5-6(Q5) |
| Oct 18 - Oct 22 | 4.7 | 4.9-Review | EXAM #2 |
| Oct 25 - Oct 39 | 5.1 | 5.2 | 5.3(Q6) |
| Nov 1 - Nov 5 | 5.4 | 5.5 | Cancelled |
| Nov 8 - Nov 12 | 5.7 | 5.8(Q7) | 6.1 |
| Nov 15 - Nov 19 | 6.2-3 | 6.3-4 | 6.4-5(Q8) |
| Nov 22 - Nov 26 | 6.5-6 | 6.6-7 | Holiday |
| Nov 29 - Dec 3 | 6.8 | Review | Exam #3 |
| Dec 6 - Dec 10 | 7.1-2 | 7.2-4(Q9) | 7.4-Review |
Homework Assignments
- Section 1.1 p. 11 Problems 1,4,9,11,15,19,29
- Section 1.2 p. 25 Problems 1-3,9,11, 19,21, 23
- Section 1.3 p. 37 Problems 1,3, 5,8,9,11,13,17,21, 27a-b
- Section 1.4 p. 47 Problems 1,4,5,7, 9, 11, 17, 21,23,25
- Section 1.5 p. 55 Problems 1,5,7,11,13,19, 23
- Section 1.7 p. 71 Problems 1,3,5,7,9,11,15-20,22,32,33.
- Section 1.8 p. 79 Problems 1,3,5,7,8,9,11,13,15,19,20.
- Section 1.9 p. 90 Problems 1,2,3,6,8,12,15,17,23.
- Section 1.10 p. 99 Problems 1,4,7,9,12; p.102:1.
- Section 2.1 p. 116 Problems 1,2,4,7,10,12,17,27,28.
- Section 2.2 p. 126 Problems 1,3,5,6,7,9,13,17,31.
- Section 2.3 p. 132 Problems 1-8,11,15,18,20,28,33.
- Section 3.1-2 p. 190 Problems 25-30,33-37; p.199:5,7,15-20,21.
- Section 3.3 p. 190:1,9,11,15,17; p.209:1,5,7,19,23; p.211:1.
- Section 4.1 p.223:1,3,5-8,9,11,15,17,21,23. 17.
- Section 4.2 p.234:1,3,7,9,13,15,17,21,28,31.
- Section 4.3 p.243:1,3,5,8,9,15,23,25.
- Section 4.4 p. 253: 1,3,5,7,9,11,13,17,27,29
- Section 4.5-6 p.260:1,3,5,9,11,13,21,29,30; p.263:1,3,5-12,25.
- Section 4.7 p.276:1,5,7,13.
- Section 4.9 p.296:1,3,5,7,11,; p.298:1.
- Section 5.1-2 p.308:1,3,5,7,17,19,23; p.317:1,3,9,13,15.
- Section 5.3 p.325:1,3,5,7,11,23-26.
- Section 5.4 p.333:1,3,7,13,17,23.
- Section 5.5 p.341:1,3,7,13,15.
- Section 5.7 p.361:1,3,5,7,9; p.370:1.
- Section 5.8 p.368:1,3 5,7,9,11,15.
- Section 6.1 p.382:1-9,13,19-22,26,27.
- Section 6.2 p.392:1-7,9,11,15,17,21.
- Section 6.3 p.400:1,3,5,7,11,13,15
- Section 6.4 p.407:1,3,5,7,9,11,15.
- Section 6.5 p.416:1,3,5,7,9,13,25.
- Section 6.6 p.425:1,7,9,15; p.444:1.
- Section 6.7 p.435:21-25.
- Section 6.8 p.443:8-12,16.
- Section 7.1 p.454:1-11 odd,13,17.
- Section 7.2 p.462:1,3,5,7,9,11,13,19,23,24.
- Section 7.4 p.481:1, 3, 5,7,9,11,12,13,15,17,18.