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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