《流動非線性及其同倫分析流體力學和傳熱(精)》編著者瓦捷拉維魯。
科學工程中的很多問題是非線性的，難以解決。傳統的解析近似方法隻對弱非線性問題有效，但無法很好地解決強非線性問題。同倫分析方法是近20年發展起來的一種有效的求解強非線性問題的解析近似方法。《流動非線性及其同倫分析：流體力學和傳熱（英文版）》介紹了同倫分析方法的*新理論進展，但不局限於方法的理論架構，也給出了大量的流體力學和傳熱中的非線性問題實例，來體現同倫分析方法的應用性。
　　《流動非線性及其同倫分析：流體力學和傳熱（英文版）》適合於物理、應用數學、非線性力學、金融和工程等領域對強非線性問題解析近似解感興趣的科研人員和研究生。

1 Introduction
References
2 Principles of Homotopy Analysis
2.1 Principles of homotopy and the homotopy analysis method.
2.2 Construction of the deformation equations
2.3 Construction of the series solution
2.4 Conditions for the convergence of the series solutions
2.5 Existence and uniqueness of solutions obtained by homotopy analysis
2.6 Relations between the homotopy analysis method and other analytical methods
2.7 Homotopy analysis method for the Swift Hohenberg equation
2.7.1 Application of the homotopy analysis method
2.7.2 Convergence of the series solution and discussion of results
2.8 Incompressible viscous conducting fluid approaching a permeable stretching surface
2.8.1 Exact solutions for some special cases
2.8.2 The case of G≠0
2.8.3 The case of G=0
2.8.4 Numerical solutions and discussion of the results.
2.9 Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet
2.9.1 Formulation of the mathematical problem
2.9.2 Exact solutions
2.9.3 Constructing analytical solutions via homotopy analysis
References

3 Methods for the Control of Convergence in Obtained Solutions
3.1 Selection of the auxiliary linear operator and base function representation
3.1.1 Method oflinear partition matching
3.1.2 Method of highest order differential matching
3.1.3 Method of complete differential matching
3.1.4 Initial versus boundary value problems
3.1.5 Additional options for the selection of an auxiliary linear operator
3.1.6 Remarks on the solution expression
3.2 The role of the auxiliary function
3.3 Selection of the convergence control parameter
3.4 0ptimal convergence control parameter value and the Lane-Emden equation of the first kind
3.4.1 Physical background
3.4.2 Analytic solutions via Taylor series
3.4.3 Analytic solutions via homotopy analysis
References

4 Additional Techniques
4.1 Construction of multiple homotopies for coupled equations
4.2 Selection of an auxiliary nonlinear operator
4.3 Validation of the convergence control parameter
4.3.1 Convergence controlparameter plots （"h-plots"）
4.3.2 Minimized residual errors
4.3.3 Minimized approximate residual errors
4.4 Multiple homotopies and the construction of solutions to the Foppl-von Karman equations governing defiections of a thin flat plate
4.4.1 Physical background
4.4.2 Linearization and construction of perturbation solutions
4.4.3 Recursive solutions for the clamped edge boundary data
4.4.4 Special case: The thin plate limit h→0,v2→1
4.4.5 Control of error and selection of the convergence control parameters
4.5 Nonlinear auxiliary operators and local solutions to the Drinfel'd-Sokolov equations
4.6 Recent work on advanced techniques in HAM
4.6.1 Mathematical properties of h-curve in the frame work of the homotopy analysis method
4.6.2 Predictor homotopy analysis method andits application to some nonlinear problems
4.6.3 An optimal homotopy-analysis approach for strongly nonlinear differential equations
4.6.4 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity
References

5 Application of the Homotopy Analysis Method to Fluid Flow Problems
6 Further Applications of the Homotopy Analysis Method
Subject Index
Author Index