Math204

Form (6)

Course Description form

Faculties and departments requiring this course (if any): Faculties of Engineering and of Science.

Objectives:  Prefer In points

1- This course is primarily designed for undergraduate students studying physics and various disciplines of engineering.

2- Deriving ODEs that describe various phenomena in physics, mechanics, chemistry, biology, etc.

3- Learning various methods for solving a great variety of differential equations.

4- Upgrading the skills of the student to understand more better the other branches physics, mechanics, chemistry, biology.

Contents: Prefer In points

1. Basic concepts: Definitions. Classifications of ODEs. Solutions types. Origin of ODEs.

2. First-order differential equations. Preliminary theory. existences and uniqueness for initial – boundary value problems. Separable variables, Homogeneous equations. Exact equations. Linear equations. Equations of Bernoulli, Ricatti. Substitutions. Picard's methods.

3. Linear differential equations of higher-order: Preliminary theory; existences and uniqueness for initial – boundary value problems. Basic concepts; Linear dependence and Linear independence, Superposition principle for homogeneous equations, fundamental set, Superposition principle for non-homogeneous equations, Constructing of a second solution from a known solution, Homogeneous equations with constant coefficients, Method of undetermined coefficients, Method of variation of parameters. Differential equations with variable coefficients, Cauchy-Euler equations.

4. Laplace Transform: Laplace transform, Inverse transform, Translation theorems, Differentiation and Integration of the Laplace Transform, Partial Fractions, Transform of derivatives, Convolution, Transform of periodic functions, Applications of Laplace transform to solve ordinary differential equations.

 Course Outcomes:

1. Knowledge:

 (Specific facts and knowledge of concepts, theories, formula etc.)

On completion of this module, students should be able to classify the

differential equations, solving a great variety of first order ODEs that describe

 models occurring  in basic science physics, chemistry, engineering, etc.

B-Cognitive Skills:

(Thinking, problem solving)

1-    The students acquires the ability to find mathematical models that describe concrete world problems.

2-    Applying the standard emanating criteria given in the course to much better understanding applied fields.

3-    Recognizing the importance of mathematics as a wonderful and power tools to better understand what the students study. 

C- Interpersonal skills and responsibilities:

(group participation, leadership, personal responsibility, ethic and moral

 behavior, capacity for  self directed learning)

The student will recognize that the various sciences form an integrated

 system and found on the other sides what  help him to better understand his

 field and opens ways of cooperation with others from other specialties, and

 then recognizes the importance of teamwork.

D- Analysis and communication:

)communication, mathematical and IT skills)

Differential equations highlight the importance of theoretical physics. This

 course help the student to better understand the physical phenomena

 through mathematical analysis. 

Assessment methods for the above elements: Discussions, Homework,

Text book: Only one

     D. G. Zill, A First Course in Differential Equations with Modeling

                       Applications, Brooks l Cole, Cengage Learning, 2009

Supplementary references

      Book Title: Elementary Differential Equations with Boundary Value Problems,

      Sixth Edition.

      Publisher: Pearson Education International,  Pearson Prentice Hill.

      Authors: C. H. Edwards   &   D. E. Penney.

      Year: 2009