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

Week #1
  • 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)
April 1st: classes begin
Week #2
  • Chapter 4: Span, subspace, and dimension
  • Chapter 5: Basis and orthogonality
  • Chapter 6: Projection onto subspaces
..
Week #3
  • 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

April 19th (Fri, 5:00 p.m.). Final day to add or drop a class;
Week #4
  • Chapter 10: Multivariable extrema via critical points
  • Chapter 11: Gradient and linear approximation
  • Chapter 12: Solving constrained optimization via Lagrange multipliers
April 25th: midterm I.
Week #5
  • Chapter 13: Linear functions, matrices, and the derivative matrix
  • Chapter 14: Linear transformations and matrix multiplication
  • Chapter 15: Matrix algebra
Week #6
  • 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
  • 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

May 13th (Monday, 5:00 p.m.): Term withdrawal deadline.
May 16th: Midterm II.
Week #8
  • 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

May 24th (Fri, 5:00 p.m.): Change of grading basis deadline.
Week #9
  • Chapter 25: Second partial derivatives and Hessian matrix
  • Chapter 26: Application of Hessian: multivariable second derivative test for local extrema
Week #10
  • Chapter 27: More applications of eigenvalues (especially singular value decomposition)
  • Review
End-Quarter Period.
Final Exam June 7th 7-10 PM


Spring 2019
Department of Mathematics, Stanford University
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