JeffGroah

An introduction to partial differential equations. The Continuity Equations, Maxwell's Laws, The Wave Equation.

Lord Kelvin's theory on the age of the Earth is explored with a spherical earth model. (Lord Kelvin used a flat Earth approximation.)

Eigenvalues and eigenvectors

Singular value decomposition

Diagonalization of Real Symmetric Matrices

Gram-Schmidt Process, Fourier Series

Inner product spaces

Diagonalization, diagonalizability, diagonalizable

Matrix representations of linear transformations

Vector space isomorphisms

Null space, range and the Dim-Dom Theorem

Linear Transformations

Coordinate, change of basis and transition matrices

Basis and Dimension

Subspaces

Vector spaces

Linear Independence

Linear combinations and finite dimensional real vector spaces. $\mathbb{R}^{2}$. R_n

Elementary Matrices

Determinants

Inverse matrices, inverse matrix method.

Homogeneous systems, Matrix algebra, vectors, applications

Linear Algebra, linear systems, solutions, elementary row operations, row echelon form, reduced row echelon form, Gaussian Elimination, Gauss-Jordan elimination, consistent, inconsistent systems, solution set

Final Exam Review

Exam 5 Review