MAT CC-07 · State Universities of Bihar

Differential and Integral Equations

Postgraduate Mathematics (CBCS)

The Syllabus

01Introduction to Initial Value ProblemsCH

02Equivalence of IVP and Integral EquationsCH

03Conversion of Higher-Order ODEs to First-Order SystemsCH

04Existence of Solutions to Initial Value ProblemsCH

05Uniqueness of Solutions to Initial Value ProblemsCH

06Classification of Integral EquationsCH

07Eigenvalues and Eigenfunctions of IECH

08Fredholm Integral Equations of the Second KindCH

09Iterative Schemes for Fredholm Integral EquationsCH

10Successive Approximations for Integral EquationsCH

11The Ascoli-Arzelà TheoremCH

12Convergence of Solutions for Families of IVPCH

13Picard-Lindelöf TheoremCH

14Peano's Existence Theorem and CorollariesCH

15Kamke's Convergence TheoremCH

16Gronwall's InequalityCH

17Maximal and Minimal Solutions of IVPsCH

18Differential InequalitiesCH

19Uniqueness Theorems for IVPsCH

20Nagumo's and Osgood's Uniqueness CriteriaCH

21Revisited Method of Successive ApproximationsCH