Week 03: Introduction to initial value problems Differential equations as mathematical models
Introduction to initial value problems
Differential equations as mathematical models
Course Material
- Week 01: Introduction to differential equations: preliminaries and classification of differential equations
- Week 02: Verification of solution, existence of unique solutions
- Week 03: Introduction to initial value problems Differential equations as mathematical models
- Week 04: First order ordinary differential equations: Basic concepts, formation and solution of differential equations
- Week 05: Separable equations, Linear equations , integrating factors, Exact Equations
- Week 06: Solution of some nonlinear first order DEs by substitution, Homogeneous Equations, Bernoulli equation, Ricaati’s equation and Clairaut equation
- Week 07: Modeling with first-order ODEs: Linear models, Nonlinear models
- Week 08: Higher order differential equations
- Week 09: Mid Term Examination
- Week 10: Reduction of order, homogeneous equations with constant coefficients
- Week 11: Nonhomogeneous equations, undetermined coefficients method, Superposition principle, Annihilator approach, variation of parameters, Cauchy-Euler equation
- Week 12: Solving system of linear DEs by elimination, solution of nonlinear DEs
- Week 13: Series Solutions: Power series, ordinary and singular points, Existence of power series solutions
- Week 14: Solutions about singular points, types of singular points, Frobenius theorem, Existence of Frobenius series solutions
- Week 15: Special functions, The Bessel, Modified Bessel, Legendre and Hermite equations and their solutions. Sturm-Liouville problems, eigen values, adjoint and self adjoint
- Week 16: Self adjoint differential equations, eigen values and eigen functions, Sturm-Liouville (S-L) boundary value problems, regular and singular S-L problems and properties
- Week 17: Final Term Exam
- Chapters 17
- Department Physics
- Teacher
Mr. M. Adeel
