MATH 461 (Linear Algebra for Scientists and Engineers)
| DESCRIPTION |
The course provides an introduction to linear algebra and
matrix theory.
It is intended primarily for engineering students. This course
cannot
be used toward the upper level math requirements for MATH/STAT
majors.
Credit will be granted for only one of the following: MATH 240, MATH
400,
MATH 461. |
| PREREQUISITES |
MATH 141 and one MATH/STAT course for which MATH 141 is a
prerequisite. |
| TOPICS |
Systems of Linear Equations
Gaussian elimination
Echelon forms
Existence and uniqueness of solutions
Homogeneous systems
Matrices
Addition, scalar multiplication,
multiplication of matrices
Elementary matrices and inversion
LU decomposition
Systems of linear equations as matrix
equations
*Partitioned matrices
Determinants and their properties
Cramer's rule
Vector Spaces
Subspaces and spanning sets
Linear independence
Basis and dimension
Row and column spaces of a matrix
Rank of a matrix
Null space of a matrix
Linear Transformations
Kernel and range
Matrix representation
Change of basis and similarity of matrices
Scalar Products and Orthogonality
Cauchy-Schwarz and triangle inequalities
Length and angles
Pythagorean theorem
Orthonormal sets
Orthogonal complements of the null space
and column space
Orthogonal projection
Least squares problems
Orthogonal matrices
Gram-Schmidt process and QR factorization
Eigenvalues
Complex eigenvalues
Diagonalization of matrices
Spectral theorem for symmetric (*hermitian)
matrices
*Quadratic forms
Positive definite matrices
*Nonnegative matrices
Applications
Including several of the following:
*Liontief Input-Output Model
*Markov Chains
*Computer Graphics
*Least squares data fitting
*Fourier Series
*Systems of Differential Equations
*Difference Equations
*Max-Min Theory for functions of several
variables (Hessian Matrix)
MATLAB use
In assigned homework through the semester
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| TEXT |
Text(s)
typically used in this course. |
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