DEPARTMENT OF MATHEMATICS



DEPARTMENT OF MATHEMATICS

SEMESTER 1436 - 1437

M 506 Ordinary and Partial Differential Equations 3(3,0)

Initial and boundary value problems for ordinary differential equations.

Numerical solutions.

Elliptic, parabolic and hyperbolic partial differential equations.

Initial and boundary value problems for second order partial differential equations.

Numerical solutions.

CHAPTER 1

Classification of DE, Methods for solving ODE

CHAPTER 2

Power series solutions of DE, Bessel’s equation, Legendre’s equations. Orthogonal functions, Sturm-Liouville problems.

CHAPTER 3

Numerical solutions of ODE, single step method: Euler, Range-Kutta methods. Milne’s and Adam- Moulton methods.

CHAPTER 4

Classification of second order PDE, solution of by separation of variable BVP using Fourier series. BVP leading to Bessel functions, BVP leading to Legendre Functions.

CHAPTER 5

Numerical solution of BVP, Finite difference method

CHAPTER 6

Numerical solution of Elliptic, Parabolic and Hyperbolic PDE.

REFERENCES

LIBRARY REFERENCE 515.3’53

1. D.G. Zill, Michael R. Cullen

Differential equations with boundary value problems, 6th Ed. PDF

2. J.R.Hanna

Fourier series and integral of boundary value problems.

3. Peter V. O’Neil

Advanced Engineering Mathematics, 7th Ed. PDF

4. Tyn Myint-U

Partial differential equations of Mathematical Physics, 2nd Ed.

5. M.R.Spiegel

Applied Differential equations 3rd Ed.

6. C.F.Gerald and P.O. Wheathey

Applied Numerical Analysis, 5th Ed.

7. Mary L. Boas

Mathematical Methods in Physical Sciences

8. Donal W. Trim

Applied Differential Equations

8. G. Strphenson

An introduction to Partial Differential Equations for science students.

9. W.E.William

Partial Differential Equations

10. P. Duchateau, D.Zachmann

Applied Partial Differential Equations

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