| 摘要 | 第1-6页 |
| Abstract | 第6-11页 |
| Chapter 1 Introduction | 第11-15页 |
| ·Research background | 第11-12页 |
| ·The first order polynomial differential equations | 第12-14页 |
| ·Organization of this dissertation | 第14-15页 |
| Chapter 2 The first order polynomial ordinary differential equations | 第15-45页 |
| ·Introduction | 第15-20页 |
| ·The linear equations about the unknown one variable functions with con-stant coefficients | 第20-24页 |
| ·Converted into the simultaneous of the first order linear ordinary differen-tial equations with constant coefficients and the quadratic equations | 第24-30页 |
| ·Three scenarios about the smoothing-solution | 第30-45页 |
| Chapter 3 The first order polynomial partial differential equations | 第45-76页 |
| ·Introduction | 第45-51页 |
| ·The linear equations about the unknown multivariate functions with con-stant coefficients | 第51-54页 |
| ·Converted into the simultaneous of the first order linear partial differential equations with constant coefficients and the quadratic equations | 第54-61页 |
| ·Three scenarios about the smoothing-solution | 第61-76页 |
| Chapter 4 The Navier-Stokes equations | 第76-116页 |
| ·Introduction | 第76-77页 |
| ·The linear equations about the unknown multivariate functions with con-stant coefficients | 第77-80页 |
| ·Converted into the simultaneous of the first order linear partial differential equations with constant coefficients and the quadratic equations | 第80-87页 |
| ·Three scenarios about the smoothing-solution | 第87-116页 |
| Chapter 5 Conclusion and discussion | 第116-117页 |
| Bibliography | 第117-126页 |
| 攻读博士学位期间撰写的论文 | 第126-127页 |
| 致谢 | 第127-128页 |
