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Math 51
Winter 2021

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

Week 1 (1/11-1/15)
[1/11 Preliminary study list deadline]
[1/11 First lecture; 1/12 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 (1/18-1/22)
[1/18 MLK day, no classes]
[1/21 Exam 1; covers through end of Week 1 topics listed above]
Chapter 4: Span, subspace, and dimension
Chapter 5: Basis and orthogonality
Chapter 6: Projection onto subspaces
Week 3 (1/25-1/29)
[1/29 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 (2/1-2/5)
[2/4 Exam 2; 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 (2/8-2/12)
Chapter 13: Linear functions, matrices, and the derivative matrix
Chapter 14: Linear transformations and matrix multiplication
Chapter 15: Matrix algebra
Week 6 (2/15-2/19)
[2/15 Presidents' Day, no classes]
[2/18 Exam 3; covers through end of Chapter 14 topics listed above]
Chapter 16: Applications of matrix algebra: Markov chains and feedback loops
Chapter 17: Multivariable Chain Rule
Week 7 (2/22-2/26)
Chapter 18: Matrix inverses and multivariable Newton's method
Chapter 19: Linear independence and the Gram-Schmidt process
Chapter 20: Matrix transpose, orthogonal matrices, and quadratic forms
Week 8 (3/1-3/5)
[3/5, 5pm: Course withdrawal and change of grading basis deadline]
[3/4 Exam 4; covers through end of Week 7 topics listed above]
Chapter 21: Systems of linear equations, column space, and null space
Chapter 22: Matrix decompositions (LU and QR)
Chapter 23: Eigenvalues and eigenvectors
Week 9 (3/8-3/12)
Chapter 24: Applications of eigenvalues: matrix powers, Spectral Theorem, and geometry of quadratic forms
Chapter 25: Hessian matrix and quadratic approximation
Chapter 26: Application of Hessian: multivariable second derivative test for local extrema
Week 10 (3/15-3/19)
[3/18 Last section; No lecture on 3/19 - Exam 5 may be taken during 3/19 lecture time (and other times).]
[3/18 Exam 5; covers through end of Chapter 26 topics listed above]
Chapter 27: More applications of eigenvalues (especially singular value decomposition) (not covered on final exam)
End of Quarter Review

Winter 2021 -- Department of Mathematics, Stanford University
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