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FACULTY OF SCIENCES - DEPARTMENT OF MATHEMATICS COURSE SYLLABUS
MATH 204: Differential Equations I
COURSE TITLE ENGLISH
CODE/NO
ARABIC CODE/NO.
CREDITS Th. Pr. Tr. Total Differential Equations I MATH 204 204 ر 3 1 3
Pre-requisites: MATH 202
Course Role in Curriculum
(Required/Elective): Required Course
Catalogue Description:
Basic concepts - First-order differential equations - Existences and Uniqueness for initial – boundary value problems - Separable variables - Homogeneous equations - Exact equations.
Linear equations - Equations of Bernoulli - Ricatti. Substitutions - Picard's methods - Linear differential equations of higher-order - Homogeneous equations with constant coefficients, Method of undetermined coefficients, Method of variation of parameters. Differential equations with variable coefficients, Cauchy-Euler equations - Laplace Transform - Applications of Laplace transform to solve ordinary differential equations.
Textbooks:
1. C. H. Edwards & D. E. Penney, Elementary Differential Equations with Boundary Value Problems, Sixth Edition. Pearson Prentice Hill, 2008.
Supplemental Materials:
Course Learning Outcomes:
By the completion of the course the student should be able to:
1. Deriving ODEs that describe various phenomena in physics, mechanics, chemistry, biology, etc.
2. Learning various methods for solving a great variety of differential equations.
3. Upgrading the skills of the student to understand more better the other branches physics, mechanics, chemistry, biology.
Topics to be Covered:
1. Basic concepts:
a. Definitions.
b. Classifications of ODEs.
c. Solutions types.
d. Origin of ODEs.
2. First-order differential equations.
a. Preliminary theory.
b. Existences and uniqueness for initial – boundary value problems.
c. Separable variables, d. Homogeneous equations.
2 e. Exact equations.
a. Linear equations.
f. Equations of Bernoulli, g. Ricatti. Substitutions.
h. Picard's methods.
3. Linear differential equations of higher-order:
a. Preliminary theory
b. Existences and uniqueness for initial – boundary value problems.
c. Basic concepts;
a. Linear dependence and Linear independence, d. Superposition principle for homogeneous equations, e. fundamental set,
f. Superposition principle for non-homogeneous equations, g. Constructing of a second solution from a known solution, h. Homogeneous equations with constant coefficients, i. Method of undetermined coefficients,
j. Method of variation of parameters.
k. Differential equations with variable coefficients, l. Cauchy-Euler equations.
4. Laplace Transform:
a. Laplace transform, b. Inverse transform, c. Translation theorems,
d. differentiation and Integration of the Laplace Transform, e. Partial Fractions,
f. Transform of derivatives, g. Convolution,
h. Transform of periodic functions,
i. Applications of Laplace transform to solve ordinary differential equations.
