Math305

Course Description form

Faculties and departments requiring this course (if any): Faculty of science.

Objectives:  Prefer In points

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

2.    The student will learn to find power series solutions for second-order linear ODEs with variable coefficients.

3.    The student will recognize and understand the special functions occurring in the solution of a variety of differential equations.

4.    This course will enhance the students' skills to comprehend the expressions involving special functions in the solutions of the problems of physics, mechanics, chemistry, biology, etc.

Contents: Prefer In points

1-The solution of the second order linear ordinary differential equations with variable coefficients will be obtained in terms of power series. These solutions lead to the definitions of new functions, commonly known as "special functions".

2-This part is devoted to the Gamma and Beta functions, two functions defined by integrals and closely related to one another. These functions are  encountered in many other contexts.

3- This part is concerned with a study of the Legendre polynomials- solutions of Legendre`s equation, which very often arises when a problem possesses spherical symmetry.

4- This part is devoted to Bessel functions. These functions occur in a variety  of applications such as loudspeaker design, optical diffraction, etc.

5-The Hermite polynomials and their applications in the quantum-mechanical harmonic oscillator. 

6- The hypergeometric functions and their relationship with other special functions. 

7-Chebyshev polynomials and their applications

Course Outcomes:

A-   Knowledge:

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

     On completion of this module, students should be able to classify the special equations, solving a great variety of the ODEs that describe models occurring  in basic science physics, chemistry, engineering, etc.

B-Cognitive Skills:

     (Thinking, problem solving)

1-    The students will be able to develop the mathematical models ssociated  with real world problems.

      2-  The standard criteria given in the course will help the students to

      understand the problems of physical sciences in a better and comprehensive

      manner.

3-    The student will realize the importance of mathematics as a wonderful and

4-    power tools to better understand what he/she studies in other fields.  

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 play a key role in the formulation of various  phenomena of  physics. This course helps the student to better understand the physical phenomena through mathematical analysis. 

Assessment methods for the above elements

Discussions, Homework, Periodic tests and final test

Text book: Only one

     Special functions for scientists and engineers Author: Bell W.W ( Van

     Nostrand )

Supplementary references

     Book Title: Introduction to ordinary Differential Equations. 

     Author:A.L.Rabenstein . 

     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.