# 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 MATH-255. Prerequisite : MATH-154 or MATH-157.

TEXTBOOK: Differential Equations & Linear Algebra , 1st Ed., by Greenberg (Adopted S05)
(Adopted F00: Differential Equations With Linear Algebra, 2nd Ed., by Goode
(Used 1/95-5/00: 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 First-order 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. Higher-order Linear Differential Equations
B. Homogeneous Linear Equations with Constant Coefficients , Undetermined Coefficients
C. Applications of Second-order 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

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