UW COLLEGES

DEPARTMENT OF MATHEMATICS

 

COURSE GUIDELINES

 

Course Title        Linear Mathematics______________________

 

Course No.     MAT 224__

 

Contact hrs/wk:  Lecture   __     Lecture/Discussion __4__     Lab  ____

 

Course Prerequisites:   A grade of C or better in MAT 223 or equivalent.

 

Catalog description:  Introduction to linear algebra, vector spaces, matrices, linear transformations, and eigenvalues. Ordinary differential equations and linear systems of differential equations. Additional topics may include Laplace transforms, Fourier series and Fourier transforms. 

 

Course content (list of topics normally covered):

 

1.       First-order ordinary differential equations

2.       Matrices and systems of linear equations

3.       Vector spaces and linear transformations: subspaces, linear independence and dependence, basis, coordinates, dimension, linear transformations and matrices, inner product spaces, orthogonal transformations, the algebra of linear transformations

4.       Eigenvalues and eigenvectors

5.       Systems of linear differential equations: the case of homogeneous equations with constant coefficients, the fundamental matrix of solutions, the matrix exponential, the non-homogeneous case, the structure of the general solution

6.       Higher-order linear differential equations: characteristic polynomial, cases of  real and distinct , real and repeating, and complex roots, linear independence of solutions, the method of undetermined coefficients

7.       The Fourier series, Fourier integral, Fourier and Laplace transforms and differential equations

 

Content-based department proficiencies:

The successful student will:

·         Be able to identify and solve first order differential equations of various types

·         Be able to identify subspaces of a vector space, identify linearly independent and linearly dependent sets of vectors, identify and construct a basis, an orthogonal and orhonormal basis, verify whether a given transformation is linear

·         Be able to solve the eigenvalue problem for a given matrix

·         Be able to solve a system of first order differential equations with constant coefficients

·         Be able to solve the standard higher-order linear differential equations

·         Be able to find Fourier series of a periodic function and Fourier integral of  an integrable function

·         Be able to apply the Fourier and Laplace transforms to solving differential equations

 

 

Colleges-wide proficiencies assigned to course:

 

Students should be able to demonstrate the following:

A. Analytical skills Performance Indicators: Students should be able to:

1. Interpret and synthesize information and ideas.

4. Select and apply scientific and other appropriate methodologies.

 

B. Quantitative skills Performance Indicators: Students should be able to:

1. Solve quantitative and mathematical problems.

2. Interpret graphs, tables, and diagrams.

 

Representative textbooks used for the course:

·         Linear Algebra and Differential Equations by Charles Cullen

·         Differential Equations matrices and models by Paul Bugl  

·         Advanced Engineering Mathematics by Erwin Kreyszig, 6th edition

 

 April 22, 2006