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Math 51
Winter 2020

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

Week 1 (1/6-1/10)
[1/6 Preliminary study list deadline]
[1/6 First lecture; 1/7 first 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 (1/13-1/17)
Chapter 4: Span, subspace, and dimension
Chapter 5: Basis and orthogonality
Chapter 6: Projection onto subspaces
Chapter 7: Application of projections: linear regression
Week 3 (1/20-1/24)
[1/24 Final study list deadline]
Chapter 8: Multivariable functions, level sets, and contour plots
Chapter 9: Partial derivatives and how to visualize them
Week 4 (1/27-1/31)
[1/30 Midterm 1, approximately 7:30pm ; roughly covers through end of Week 3 topics listed above]
Chapter 10: Multivariable extrema via critical points
Midterm 1 Review
Chapter 11: Gradient and linear approximation
Week 5 (2/3-2/7)
Chapter 12: Solving constrained optimization via Lagrange multipliers
Chapter 13: Linear functions, matrices, and the derivative matrix
Chapter 14: Linear transformations and matrix multiplication
Week 6 (2/10-2/14)
Chapter 15: Matrix algebra
Chapter 16: Applications of matrix algebra: Markov chains and feedback loops
Chapter 17: Multivariable Chain Rule
Week 7 (2/17-2/21)
[2/20 Midterm 2, approximately 7:30pm ; covers through end of Week 6 topics listed above]
Chapter 18: Matrix inverses and multivariable Newton's method
Chapter 19: Linear independence and the Gram-Schmidt process
Week 8 (2/24-2/28)
[2/28, 5pm: Course withdrawal and change of grading basis deadline]
Chapter 20: Matrix transpose, orthogonal matrices, and quadratic forms
Chapter 21: Systems of linear equations, column space, and null space
Chapter 22: Matrix decompositions (LU and QR)
Week 9 (3/2-3/6)
Chapter 23: Eigenvalues and eigenvectors
Chapter 24: Applications of eigenvalues: matrix powers, Spectral Theorem, and geometry of quadratic forms
Chapter 25: Second partial derivatives and Hessian matrix
Chapter 26: Application of Hessian: multivariable second derivative test for local extrema
Week 10 (3/9-3/13)
[3/12 Last section; 3/13 last lecture]
[3/17 Final Exam, 12:15-3:15pm; comprehensive but more heavily emphasizes topics since Midterm 2]
Chapter 25 and 26, leftovers
Chapter 27: More applications of eigenvalues (especially singular value decomposition) (not covered on final exam)
Final Exam Review

Winter 2020 -- Department of Mathematics, Stanford University
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