世界著名数学家R.H.Bing曾指出： 大多数学生将不是从事研究的数学家，大多数不会到达前沿——但他们能更多地欣赏数学，如果他们知道前沿就在那里，知道它(指前沿)不是不可达到的，对它偶一瞥见并认识到它正在被接近了——有时是平稳的，但常常是一阵阵的。 本书就是这样一部试图让学生欣赏数学，了解前沿的英文版数学专著。 本书的中文书名或可译为《抛物型狄拉克算子和薛定谔方程：不定常薛定谔方程的抛物型狄拉克算子及其应用》。

Introduction
1 Preliminaries
1.1 Clifford Algebras
1.1.1 Real Clifford algebras
1.1.2 Complex Clifford algebra
1.1.3 Function spaces
1.2 Clifford analysis
1.2.1 Teodorescu operator
1.2.2 Clifford analysis using the Teodorescu operator
2 Continuous calculus operator
2.1 Time-dependent operators
2.1.1 Factorization of time-dependent operators
2.1.2 Fischer decomposition for the homogeneous operator D
2.1.3 Powers of D
2.2 Operator calculus for the SchrSdinger operator
2.2.1 Regularization of the fundamental solution
2.2.2 Regularized Teodorescu and Cauchy-Bitsadze operators
2.2.3 Hypoelliptic analysis
2.2.4 Lp-decomposition
3 The non-linear Schrodinger problem
3.1 Resolution of the NLS problem via an iterative method
3.1.1 Existence and uniqueness of solution
3.1.2 Convergent iterative method
3.2 Discrete fundamental solution for time-evolution problems
3.2.1 Quaternionic matrix representation of the Witt basis
3.2.2 Finite differences and time evolution operators
3.2.3 Discrete symbol of the Laplace operator
3.2.4 Discrete fundamental solutions
3.3 Discrete operator calculus
3.3.1 Behavior of the discrete fundamental solution
3.3.2 Discrete operators
3.3.3 Numerical examples
Conclusion
Appendix
A Hypoelliptic Theory
A.1 Definition and main properties
A.2 Sufficient conditions for hypoenipticity
Bibliography
Index
编辑手记