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Students should use
ODTU-Class
There will be a total of 42 one hour units in the course. Each week, three units will be taught.
The contents of each unit are listed below, where the section numbers refer to the course textbook by H. Anton. Course lectures focus on chapters 1-2 and 4-8 of the textbook with occasional additional topics from chapter 9 as well as applications from chapter 11 inserted at appropriate areas. Units marked * may be omitted to save time if necessary.
Note: This schedule may be modified/reorganized as the class progresses.
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Week 0:
Feb.17-18 |
0 | Introduction to the Course |
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Week 1:
Feb.21-25 |
1 |
Chapter 1. Systems of Linear Equations and Matrices
§1.1 Introduction to Systems of Linear Equations
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| 2 | §1.2 Gaussian Elimination (Gauss) | |
| 3 | §1.2 Gaussian Elimination (Gauss-Jordan) | |
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Week 2:
Feb.28-Mar.4 |
4 | §1.2 Gaussian Elimination (more examples) |
| 5 |
§1.3 Matrices and Matrix Operations (Matrix Multiplication) Application: §11.7 Graph Theory (Thm 11.7.1) |
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| 6 |
§1.3 Matrices and Matrix Operations (Sum, Transpose) §1.4 Inverses; Rules of Matrix Arithmetic (selected proofs) |
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Week 3:
Mar.7-11 |
7 | §1.5 Elementary Matrices and a Method for Finding A-1 (Finding A-1) |
| 8 |
§1.5 Elementary Matrices and a Method for Finding A-1 (Elementary matrices) Additional Topic: §9.9 LU Decomposition |
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| 9 |
§1.6 Further Results on Systems of Equations and Invertibility (summary) Chapter 2. Determinants
§2.1 Determinants by Cofactor Expansion
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Week 4:
Mar.14-18 |
10 |
§2.1 Determinants by Cofactor Expansion (cont) |
| 11 |
§2.2 Evaluating Determinants by Row Reduction §2.3 Properties of the Determinant Function (simplified proofs, stop at Thm 2.3.5) |
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| 12 | Application: §11.1 Curves Through Points | |
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Week 5:
Mar.21-25 |
13 |
Chapter 4. Euclidean Vector Spaces
§4.1 Euclidean n-Space §4.2 Linear Transformations from Rn to Rm |
| 14 | §4.3 Properties of Linear Transformations from Rn to Rm | |
| 15 |
§4.4 Linear Transformations and Polynomials Chapter 5. General Vector Spaces
§5.1 Real Vector Spaces
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Week 6:
Mar.28-Apr.1 |
16 | §5.3 Linear Independence |
| 17 |
§5.2 Subspaces §5.4 Basis and Dimension |
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| 18 |
§5.4 Basis and Dimension (cont) §5.5 Row Space, Column Space, and Nullspace |
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| EXAM 1: Saturday, April 2, 10:00-12:00 SZ-23, 24, 25 |
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Week 7:
Apr.4-8 |
19 |
§5.5 Row Space, Column Space, and Nullspace (cont) Application: §11.2 Electrical Networks |
| 20 | §5.6 Rank and Nullity | |
| 21 |
Chapter 6. Inner Product Spaces
§6.1 Inner Products §6.2 Angle and Orthogonality in Inner Product Spaces |
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Week 8:
Apr.11-15 |
22 | §6.3 Orthonormal Bases; Gram-Schmidt Process |
| 23 | §6.3 QR-Decomposition | |
| 24 |
§6.4 Best Approximation; Least Squares Additional Topic: §9.3 Least Squares Fitting to Data |
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Week 9:
Apr.18-22 |
25* | Application: §11.20* A Least Squares Model for Human Hearing |
| 26* | Review* | |
| 27 |
Chapter 7. Eigenvalues, Eigenvectors
§7.1 Eigenvalues and Eigenvectors Additional Topic: §9.2 Geometry of Linear Operators on R2 |
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Week 10:
Apr.25-29 |
28 | §7.1 Eigenvalues and Eigenvectors (cont) |
| 29 | §7.2 Diagonalization | |
| 30 |
§7.2 Diagonalization (cont) Application: §11.6 Markov Chains |
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Week 11:
May 2-6 |
31 | Generalized Eigenvectors and Jordan Form (reference to be added) |
| 32 |
§6.6 Orthogonal Matrices §7.3 Orthogonal Diagonalization |
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| 33 |
Chapter 8. Linear Transformations
§8.1 General Linear Transformations
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| EXAM 2: Saturday, May 7, 10:00-12:00 SZ-23, 24, 25 |
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Week 12:
May 9-13 |
34 | §8.2 Kernel and Range |
| 35 | §8.3 Inverse Linear Transformations | |
| 36 |
§6.5 Change of Basis §8.4 Matrices of General Linear Transformations |
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Week 13:
May 16-20 |
37 | §8.5 Similarity |
| 38 | §8.6 Isomorphism | |
| 39 |
Additional Topics and Applications
§9.5 Quadric Forms §9.6 Diagonalizing Quadratic Forms; Conic Sections |
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Week 14:
May 23-27 |
40 |
§9.6 Diagonalizing Quadratic Forms; Conic Sections (cont) §9.7 Quadric Surfaces |
| 41* | §11.11* Computer Graphics | |
| 42* | Review* | |