Homotopy analysis method in nonlinear differential equations

Part I. Basic Ideas and Theorems -- Introduction -- Basic Ideas of the Homotopy Analysis Method -- Optimal Homotopy Analysis Method -- Systematic Descriptions and Related Theorems -- Relationship to Euler Transform -- Some Methods Based on the HAM -- Part II. Mathematica Package BVPh and Its Applications -- Mathematica Package BVPh -- Nonlinear Boundary-value Problems with Multiple Solutions -- Nonlinear Eigenvalue Equations with Varying Coefficients -- A Boundary-layer Flow with an Infinite Number of Solutions -- Non-similarity Boundary-layer Flows -- Unsteady Boundary-layer Flows -- Part III. Applications in Nonlinear Partial Differential Equations -- Applications in Finance: American Put Options -- Two and Three Dimensional Gelfand Equation -- Interaction of Nonlinear Water Wave and Nonuniform Currents -- Resonance of Arbitrary Number of Periodic Traveling Water Waves