part PART I BASIC IDEAS -- chapter 1 Introduction -- chapter 2 Illustrative description -- chapter 3 Systematic description -- chapter 4 Relations to some previous analytic methods -- chapter 5 Advantages, limitations, and open questions -- part PART II APPLICATIONS -- chapter 6 Simple bifurcation of a nonlinear problem -- chapter 7 Multiple solutions of a nonlinear problem -- chapter 8 Nonlinear eigenvalue problem -- chapter 9 Thomas-Fermi atom model -- chapter 10 Volterra's population model -- chapter 11 Free oscillation systems with odd nonlinearity -- chapter 12 Free oscillation systems with quadratic nonlinearity -- chapter 13 Limit cycle in a multidimensional system -- chapter 14 Blasius viscous ow -- chapter 15 Boundary-layer ows with exponential property -- chapter 16 Boundary-layer ows with algebraic property -- chapter 17 Von Ka�rma�n swirling viscous ow -- chapter 18 Nonlinear progressive waves in deep water.