Table of contents (16 chapters)

1. Front Matter

   Pages i-xv

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2. Basic Ideas and Theorems

   1. Front Matter

      Pages 1-1

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   2. 

      Book Chapter

      Pages 3-14

      Introduction

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   3. 

      Book Chapter

      Pages 15-94

      Basic Ideas of the Homotopy Analysis Method

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   4. 

      Book Chapter

      Pages 95-129

      Optimal Homotopy Analysis Method

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   5. 

      Book Chapter

      Pages 131-187

      Systematic Descriptions and Related Theorems

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   6. 

      Book Chapter

      Pages 189-221

      Relationship to Euler Transform

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   7. 

      Book Chapter

      Pages 223-235

      Some Methods Based on the HAM

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3. Mathematica Package BVPh and Its Applications

   1. Front Matter

      Pages 237-237

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   2. 

      Book Chapter

      Pages 239-284

      Mathematica Package BVPh

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   3. 

      Book Chapter

      Pages 285-314

      Nonlinear Boundary-value Problems with Multiple Solutions

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   4. 

      Book Chapter

      Pages 315-361

      Nonlinear Eigenvalue Equations with Varying Coefficients

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   5. 

      Book Chapter

      Pages 363-381

      A Boundary-layer Flow with an Infinite Number of Solutions

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   6. 

      Book Chapter

      Pages 383-401

      Non-similarity Boundary-layer Flows

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   7. 

      Book Chapter

      Pages 403-421

      Unsteady Boundary-layer Flows

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4. Applications in Nonlinear Partial Differential Equations

   1. Front Matter

      Pages 423-423

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   2. 

      Book Chapter

      Pages 425-459

      Applications in Finance: American Put Options

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   3. 

      Book Chapter

      Pages 461-491

      Two and Three Dimensional Gelfand Equation

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   4. 

      Book Chapter

      Pages 493-522

      Interaction of Nonlinear Water Wave and Nonuniform Currents

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   5. 

      Book Chapter

      Pages 523-562

      Resonance of Arbitrary Number of Periodic Traveling Water Waves

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5. Back Matter

   Pages 563-565

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