DIFFERENTIAL EQUATIONS WITH LINEAR ALGEBRA
COURSE DESCRIPTION: Differential equations : first order
and higher order equations, systems of
linear differential equations. Linear algebra: matrices, determinants, systems
of linear equations, vector
spaces, linear transformations , eigenvalues, eigenvectors. Credit cannot be
given for both MATH 250
and MATH255. Prerequisite : MATH154 or MATH157.
TEXTBOOK: Differential Equations & Linear Algebra , 1^{st }Ed., by Greenberg
(Adopted S05)
(Adopted F00: Differential Equations With Linear Algebra, 2^{nd} Ed., by Goode
(Used 1/955/00: Rabenstein, Elementary Differential Equations with Linear
Algebra, 4th Ed.,
Harcourt/Brace, 1992.
COURSE OBJECTIVES: The student who successfully completes this course will:
1. understand and apply the basic principles of matrices and determinants.
2. understand and apply the basic principles of vector spaces and linear
transformations.
3. understand and apply the basic principles of solving first order differential
equations.
4. understand and apply the basic principles of higher order linear differential
equations.
5. understand and apply the basic principles of solving systems of linear
differential equations.
6. be able to identify engineering problems that can be solved using linear
algebra and differential
equations.
COURSE OUTLINE:
I. Introduction to Differential Equations
A. Identification and Solution of Exact , Separable, Homogeneous, Linear, and
Bernoulli
Equations
B. Applications of Firstorder Equations
II. Matrices and Determinants
A. Systems of Linear Equations, Homogeneous Systems, and Applications
B. Matrices and Vectors, Matrix Multiplication , and Some Special Matrices
C. Determinants, Properties of Determinants , Cofactors, Cramer' s Rule
D. The Inverse of a Matrix
III. Vector Spaces and Linear Transformations
A. Vector Spaces, Subspaces, Linear Dependence and Independence
B. Basis, Dimension, Wronskian
C. Basic Properties of Linear Transformations, Orthogonal Transformations
IV. Eigenvalues and Eigenvectors
A. Eigenvalues, Eigenvectors of Real Matrices
B. Diagonalization of Real Symmetric Matrices
V. Linear Differential Equations
A. Higherorder Linear Differential Equations
B. Homogeneous Linear Equations with Constant Coefficients , Undetermined
Coefficients
C. Applications of Secondorder Linear Differential Equations
VI. The Laplace Transform
A. Definition and Basic Properties, Convolutions, Laplace Transform Solution of
Linear
Differential Equations
VII. System of Linear Differential Equations
A. Homogeneous Linear Systems with Constant Coefficients, Two Equations in Two
Unknown Functions
Start solving your Algebra Problems
in next 5 minutes!




Algebra Helper
Download (and optional CD)
Only $39.99

Click to Buy Now:
OR






2Checkout.com is an authorized reseller
of goods provided by Sofmath


Attention: We are
currently running a special promotional offer
for AlgebraAnswer.com visitors  if you order
Algebra Helper by midnight of
September 17th
you will pay only $39.99
instead of our regular price of $74.99  this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
order page.
If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better  Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
Step 1
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
 simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)
 factoring and expanding expressions
 finding LCM and GCF

(simplifying, rationalizing complex denominators...)
 solving linear, quadratic and many other equations
and inequalities
(including basic logarithmic and exponential equations)
 solving a system of two and three linear equations
(including Cramer's rule)
 graphing curves (lines, parabolas, hyperbolas, circles,
ellipses, equation and inequality solutions)
 graphing general functions
 operations with functions (composition, inverse, range, domain...)
 simplifying logarithms
 basic geometry and trigonometry
(similarity, calculating trig functions, right triangle...)
 arithmetic and other prealgebra topics
(ratios, proportions, measurements...)
ORDER NOW!




Algebra Helper
Download (and optional CD)
Only $39.99

Click to Buy Now:
OR






2Checkout.com is an authorized reseller
of goods provided by Sofmath





"It
really helped me with my homework. I was
stuck on some problems and your software walked me
step by step through the process..." 
C. Sievert, KY
 



Sofmath
19179 Blanco #105234 San Antonio, TX 78258

Phone:
(512) 7885675 Fax: (512) 5191805
  