Externally indexed torrent

If you are the original uploader, contact staff to have it moved to your account

Textbook in PDF format

Math 51 course text prepared by the Stanford University Math Department
Last modified on March 10, 2021
Introduction
Applications
Advice on studying, homework, and exams for math in college, and tutoring/online resources
Preparedness for Math 51
Advice to Instructors
Geometry of vectors and projections
Vectors, vector addition, and scalar multiplication
Vector geometry in Rn and correlation coefficients
Planes in R3
Span, subspaces, and dimension
Basis and orthogonality
Projections
Applications of projections in Rn: orthogonal bases of planes and linear regression
Multivariable functions and optimization
Multivariable functions, level sets, and contour plots
Partial derivatives and contour plots
Maxima, minima, and critical points
Gradients, local approximations, and gradient descent
Constrained optimization via Lagrange multipliers
Geometry and algebra of matrices
Linear functions, matrices, and the derivative matrix
Linear transformations and matrix multiplication
Matrix algebra
Applications of matrix algebra: population dynamics, PageRank, and gambling
Multivariable Chain Rule
Matrix inverses and multivariable Newton's method for zeros
Further matrix algebra and linear systems
Linear independence and the Gram–Schmidt process
Matrix transpose, quadratic forms, and orthogonal matrices
Linear systems, column space, and null space
Matrix decompositions: QR-decomposition and LU-decomposition
Eigenvalues and second partial derivatives
Eigenvalues and eigenvectors
Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers
The Hessian and quadratic approximation
Grand finale: application of the Hessian to local extrema, and bon voyage
More eigenvalue applications: ODE systems, population dynamics, SVD (optional)
Appendices
Review of functions
Further details on linear algebra results (optional)
Equivalence of two perspectives on ellipses and hyperbolas (optional)
Google's PageRank algorithm (optional)
General determinants (optional)
The cross product (optional)
Neural networks and the multivariable Chain Rule (optional)
The QR algorithm (optional)
Newton's method for optimization (optional)
Hessians and chemistry (optional)
References