Course Description
Ordinary differential equation: Introduction to ordinary differential equations (classification and creation), ODEs of first order, separable equations, other methods for first order equations, ODEs of second order, general solution of homogenous and non-homogenous linear equations of second order.
Special functions : Review of power series solution for differential equations, Gamma and Beta functions, the simple pendulum, the error function, hypergeometric functions, orthogonal polynomials (Legendre polynomials ) and their associated functions, Bessel functions.
Laplace transforms and its applications in solving the ODEs
Course Objectives & Outcomes
Objectives
- Classify ordinary differential equation.
- Solve ordinary differential equations of first, second and higher orders,
- Provide student with advance skills of solving differential equations.
- Identify student to the special functions and their use in solving physical problems.
Outcomes: Upon successful completion of this course the student will be able to:
- Mention examples of different kind of ODEs.
- Apply different methods for solving ODEs.
- Solve ODEs, initial value problems and boundary value problems.
- Solve differential equations using power series
- Define Gamma and Beta functions, and derive the relations between them.
- Define Hypergeometric functions, derive their integral formulas and verify the relations of hypergeometric functions and other special functions and their applications.
- Distinguish orthogonal polynomials.
- Define Legendre, Hermite and Laguerre polynomials, their differential equations. Derive their generating functions and relate orthogonality properties and write the recurrence relations between orthogonal polynomials and their derivatives.
- Describe the three kinds of Bessel functions and their properties, and present their integral formulas.
References
- Mary L. Boas, (2006), Mathematical methods in the physical sciences, Third Edition, John Wiley and Sons., ISBN: 0-471-19826-9.
Course ID: MATH 308
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 2 | 2 | 4 | Calculus III |
---|