Course Description
Review of power series solution for differential equations, Gamma and Beta functions, Hypergeometric Functions, Orthogonal Polynomials (Legendre, Hermite and Lagurre) and their associated functions, Bessel functions.
Course Objectives & Outcomes
Objectives
- Provide student with advance skills of solving differential equations
- Identify student to the special functions and their use in solving physical problems.
Outcomes
On successful completion of the course, the student will be able to
- Solve differential equations using power series.
- Define Gamma and Beta functions, and derive the relation between them.
- Define Hypergeometric functions, present their Integral formula and verify the relations of hypergeometric functions and other special functions and their applications.
- Specify Orthogonal Polynomials
- Define Legendre, Hermite and Laguerre polynomials, their differential equations. Derive their generating functions, verify orthogonality properties and write the recurrence relations between Orthogonal polynomials and their derivatives
- Characterize the three kinds of Bessel functions and their properties. Solve Bessel equations. And present their integral formula.
References
1. Lebedev N. (1972) Special Functions & Their Applications, Dover Books on Mathematics, ISBN-10: 0486606244 , ISBN-13: 978-0486606248.
2. Bell W. W. (2004) Special Functions for Scientists and Engineers, Dover Books on Mathematics, ISBN-10: 0486435210, ISBN-13: 978-0486435213.
3. . Sneddon I. N. (1956) Special Functions of Mathematical Physics and Chemistry, Oliver and Boyd, ISBN 10: 0050013343, ISBN 13: 9780050013342
Course ID: MATH 402
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 4 | 4 | 4 | MATH 302 |
---|