Instructor: Shiang Tang
Course on canvas.dartmouth.edu.⇗
Tentative schedule
Week 1
Mon, 3/25: 1.1, Introduction (Read: Appendix C and Appendix D through Theorem D.1)
Wed, 3/27: 1.2 Vector Spaces
Fri, 3/29: 1.3, Subspaces
Week 2
Mon, 4/1: 1.4, Linear Combinations and Systems of Linear Equations
Wed, 4/3: 1.5, Linear Dependence and Linear Independence (HW 1 due before class, Read: Theorem 1.7 and its proof)
Fri, 4/5: 1.6, Bases and Dimension (Read: Theorem 1.10, Corollary 2 on p.48-49, Corollary on p.51)
Week 3
Mon, 4/8: 2.1, Linear Transformations (read: Appendix B on functions, especially the notion of range, one-to-one, and onto)
Tue, 4/9: Exam 1 during X-hr, 1.1-1.6
Wed, 4/10: 2.1, Null Spaces and Ranges (HW 2 due before class)
Fri, 4/12: 2.2, The Matrix Representation of a Linear Transformation
Week 4
Mon, 4/15: 2.3, Composition of Linear Transformations and Matrix Multiplication (read: Theorem 2.15(a)(b) and Theorem 2.16)
Wed, 4/17: 2.4, Invertibility and Isomorphisms (read Thm 2.18 and its corollaries. HW 3 due before class)
Fri, 4/19: 2.5, The Change of Coordinate Matrix (read: 3.1)
Week 5
Mon, 4/22: 3.2, The Rank of a Matrix and Matrix Inverses (read: Cor 2 on p.158, p.161)
Wed, 4/24: 3.2, Continued, 3.3, Systems of Linear Equations - Theoretical Aspects (HW 4 due before class)
Read before Friday: Ex 6 on p.163, from p.182 "We now describe" to right before "Of all the methods" on p.186.
Fri, 4/26: 3.4, Systems of Linear Equations - Computational Aspects (read: 4.1, Determinants of Order 2)
Week 6
Mon, 4/29: 4.2, Determinants of Order n
Tue, 4/30: Exam 2 during X-hr, 2.1-3.4
Wed, 5/1: 4.2 continued, 4.3, Properties of Determinants (HW 5 due before class)
Fri, 5/3: 5.1, Eigenvalues and Eigenvectors
Week 7
Mon, 5/6: 5.2, Diagonalizability
Wed, 5/8: 5.4, Invariant Subspaces and the Cayley-Hamilton Theorem (read: Thm 5.21-5.22. HW 6 due before class)
Fri, 5/10: 6.1, Inner Products and Norms
Week 8
Mon, 5/13: 6.2, The Gram-Schmidt Orthogonalization Process
Tue, 5/14: Exam 3 during X-hr, 4.1-5.4
Wed, 5/15: 6.2, Orthogonal Complements, 6.3, The Adjoint of a Linear Operator (HW 7 due before class. Last day to withdraw)
Fri, 5/17: 6.3 continued: Adjoints and Least Squares
Week 9
Mon, 5/20: 6.4, Normal and Self-Adjoint Operators
Wed, 5/22: 6.4, continued: Diagonalizing Self-Adjoint Operators (HW 8 due before class)
Fri, 5/24: Review for final
Week 10
Mon, 5/27: No class
Wed, 5/29: In-class office hours
Final Exam: Sun, 6/2, 11:30-14:30