Preface. 1: First Order Differential Equations. 1.0. Introduction. 1.1. Method of Upper and Lower Solutions. 1.2. Method of Quasilinearization. 1.3. Extensions. 1.4. Generalizations. 1.5. Refinements. 1.6. Notes. 2: First Order Differential Equations. (Cont.) 2.0. Introduction. 2.1. Periodic Boundary Value Problems. 2.2. Anti-Periodic Boundary Value Problems. 2.3. Interval Analysis and Quasilinearization. 2.4. Higher Order Convergence. 2.5. Another Refinement of Quasilinearization. 2.6. Extension to System of Differential Equations. 2.7. Notes. 3: Second Order Differential Equations. 3.0. Introduction. 3.1. Method of Upper and Lower Solutions. 3.2. Extension of Quasilinearization. 3.3. Generalized Quasilinearization. 3.4. General Second Order BVP. 3.5. General Second Order BVP (cont.). 3.6. Higher Order Convergence. 3.7. Notes. 4: Miscellaneous Extensions. 4.0. Introduction. 4.1. Dynamic Systems on Time Scales. 4.2. Integro-Differential Equations. 4.3. Functional Differential Equations. 4.4. Impulsive Differential Equations. 4.5. Stochastic Differential Equations. 4.6. Differential Equations in a Banach Space. 4.7. Notes. References. Index.

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