LINEARITY

and the Mathematics of Several Variables

by

Stephen A. Fulling

with the assistance of

Michael N. Sinyakov and Sergei V. Tishchenko

THE BOOK IS NOW PUBLISHED BY WORLD SCIENTIFIC PUBLISHING COMPANY.

Cover ._._. Title page

THE OBSOLETE ON-LINE FILES HAVE BEEN ERASED TO FREE UP DISK SPACE.

(c) Copyright S. A. Fulling 1995-9

  1. Vectors
    1. Vectors that You Know
    2. Lines and Planes
    3. Points: A Deeper Look
    4. Curves and Tangent Vectors
  2. Matrices
    1. Linear Systems and Matrices
    2. Matrix Algebra
    3. Inverses
    4. Functions and Gradient Vectors
    5. Elementary Determinants
  3. Vector Spaces and Linear Functions
    1. The Definition of a Vector Space
    2. Linear Functions
    3. Nonlinear Functions
    4. Differentials
    5. The Chain Rule
  4. Bases
    1. The Basis Concept: Independence and Span
    2. Local Bases Associated with a Coordinate System
    3. Dimension
    4. Coordinates with Respect to a Basis
    5. Change of Basis
  5. Subspaces and Linear Equations
    1. Subspaces
    2. Subspaces Associated with a Linear Function: Kernel and Range
    3. Linear Equations: The Superposition Principles
    4. Rank
    5. Implicit and Inverse Functions
  6. Inner Products and Differential Vector Calculus
    1. Inner Products and Norms
    2. Orthogonality
    3. The Geometry of Curves
    4. Nabla: The Vector Differential Operations
  7. Determinants and Integral Vector Calculus
    1. Properties of Determinants
    2. Volume, Rotations, and All That: Geometrical Significance of Determinants and Antisymmetry
    3. Jacobi's Theorem: Changing Variables in Multiple Integrals
    4. Surface Integrals -- Definition
    5. The Integral Theorems of Vector Analysis
    6. Direct Methods of Evaluating Line and Surface Integrals
  8. Eigenvectors and Diagonalization
    1. Eigenvalues and Eigenvectors
    2. Diagonalization of Real, Symmetric Matrices
    3. A Note on History

Go to home pages: Math 311 ._._. Math Dept ._._. University

Last updated Tue 25 Jul 00