Preliminaries: Introduction and formulation, classification of differential equations Existence
Course Material
- Preliminaries: Introduction and formulation, classification of differential equations Existence
- Existence and uniqueness of solutions
- Introduction of initial value and boundary value problems
- First order ordinary differential equations: Basic concepts, formation and solution of differential equations
- Separable variables, Exact Equations, Homogeneous Equations, Linear equations, integrating factors
- Some nonlinear first order equations with known solution, differential equations of Bernoulli and Ricaati type,Clairaut equation
- Modeling with first-order ODEs, Basic theory of systems of first order linear equations
- Homogeneous linear system with constant coefficients, Non homogeneous linear system,Second and higher order linear differential equations
- Mid Term Exam
- 9. Initial value and boundary value problems, Homogeneous and non-homogeneous equations
- 10. Superposition principle, homogeneous equations with constant coefficients, Linear independence and Wronskian
- Nonhomogeneous equations, undetermined coefficients method, variation of parameters, Cauchy-Euler equation
- Modeling. Sturm-Liouville problems: Introduction to eigen value problem, adjoint and self adjoint operators
- Self adjoint differential equations, eigen values and eigen functions, Sturm-Liouville (S-L) boundary value problems, regular and singular S-L problems, properties ofregular S-L problems
- 14. Series Solutions: Power series, ordinary and singular points, types of singular points ,Existence of power series solutions
- 15. Frobenius theorem, Existence of Frobenius series solutions, solutions about singular points
- 16. The Bessel, Modified Bessel, Legendre and Hermite equations and their solutions
- Final Term Exam
- Book
- Solution
- Chapters 20
- Department Mathematics(SCB)
- Teacher
Mr. Muhammad Shakeel Nawaz
