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The schedule of topics is tentative and will be adjusted as necessary.
- Week 1 (3/30-4/3)
- [3/30 Preliminary study list deadline]
- [3/30 First lecture; 3/31 first discussion section]
Chapter 1: Vectors and related algebra (addition, scalar multiplication)
Chapter 2: Vector geometry (length, dot product, angle) and correlation
Chapter 3: Many ways to think about planes in space (algebraic and geometric)
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- Week 2 (4/6-4/10)
Chapter 4: Span, subspace, and dimension
Chapter 5: Basis and orthogonality
Chapter 6: Projection onto subspaces
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- Week 3 (4/13-4/17)
- [4/17 Final study list deadline]
Chapter 7: Application of projections: linear regression
Chapter 8: Multivariable functions, level sets, and contour plots
Chapter 9: Partial derivatives and how to visualize them
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- Week 4 (4/20-4/24)
- [4/23 Exam 1, 7:30-9:30pm; covers through end of Week 3 topics listed above]
Chapter 10: Multivariable extrema via critical points
Chapter 11: Gradient and linear approximation
Chapter 12: Solving constrained optimization via Lagrange multipliers
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- Week 5 (4/27-5/1)
Chapter 13: Linear functions, matrices, and the derivative matrix
Chapter 14: Linear transformations and matrix multiplication
Chapter 15: Matrix algebra
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- Week 6 (5/4-5/8)
Chapter 16: Applications of matrix algebra: Markov chains and feedback loops
Chapter 17: Multivariable Chain Rule
Chapter 18: Matrix inverses and multivariable Newton's method
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- Week 7 (5/11-5/15)
- [5/14 Exam 2, 7:30-9:30pm; covers through end of Chapter 17 topics]
Chapter 19: Linear independence and the Gram-Schmidt process
Chapter 20: Matrix transpose, orthogonal matrices, and quadratic forms
Chapter 21: Systems of linear equations, column space, and null space
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- Week 8 (5/18-5/22)
- [5/22 Course withdrawal and change of grading basis deadline]
Chapter 22: Matrix decompositions (LU and QR)
Chapter 23: Eigenvalues and eigenvectors
Chapter 24: Applications of eigenvalues: matrix powers, Spectral Theorem, and geometry of quadratic forms
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- Week 9 (5/25-5/29)
- [5/25 Memorial Day; no lecture]
Chapters 25&26: Hessian matrix, quadratic approximation, and multivariable second derivative test for local extrema (days 1 and 2)
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- Week 10 and Exam Week (6/1-6/6)
- [6/2 Last section; 6/3 last lecture (last opportunity to arrange Incomplete)]
- [6/6: Final Exam, 12:15-3:15pm: comprehensive through end of Chapter 26 topics, but more heavily emphasizes topics since Exam 2]
Chapter 27: More applications of eigenvalues (especially singular value decomposition) (not covered on final exam)
End of Quarter Review
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