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Math 51
Spring 2024

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The schedule of topics is tentative and will be adjusted as necessary.

Week 1 (4/1-4/5)
[4/1 Preliminary study list deadline]
[4/1 First lecture; 4/2 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)
Week 2 (4/8-4/12)
Chapter 4: Span, subspace, and dimension
Chapter 5: Basis and orthogonality
Chapter 6: Projection onto subspaces
Week 3 (4/15-4/19)
[4/19 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
Week 4 (4/22-4/26)
[4/25 Exam 1, 8-10pm; 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
Week 5 (4/29-5/3)
Chapter 13: Linear functions, matrices, and the derivative matrix
Chapter 14: Linear transformations and matrix multiplication
Chapter 15: Matrix algebra
Week 6 (5/6-5/10)
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
Week 7 (5/13-5/17)
[5/16 Exam 2, 8-10pm; 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
Week 8 (5/20-5/24)
[5/24 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
Week 9 (5/27-5/31)
[5/27 Memorial Day; no lecture]
Chapter 25: Hessian matrix and quadratic approximation
Chapter 26: Application of Hessian: multivariable second derivative test for local extrema
Week 10 and Exam Week (6/3-6/7)
[6/4 Last section; 6/5 last lecture (last opportunity to arrange Incomplete)]
[6/8: Final Exam, 12:15-3:15pm: comprehensive through end of Chapter 26 topics, but more heavily emphasizes topics since Exam2]
Chapter 27: More applications of eigenvalues (especially singular value decomposition) (not covered on final exam)
End of Quarter Review

Spring 2024 -- Department of Mathematics, Stanford University
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