William E. Boyce and Richard C. DiPrima

本书以清晰，准确的语言书写，使学生能够理解，并减少了明确陈述的定理和定义的数量，包括对边值问题和偏微分方程的彻底处理。

Numerical Methods for Ordinary Differential Equations - J.C. Butcher (2003) WW.djvu

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time. Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.

Differential Equations are somewhat pervasive in the description of natural phenomena and the theory of Ordinary Differential Equations is a basic framework where concepts, tools and results allow a systematic approach to knowledge. This same book aims to give a concrete proof of how the modeling of Nature is based on this theory and beyond. This appendix is intended to provide some concepts and results that are used in the text, referring to the student background and to textbooks for a full acquaintance of the material. We actually mention [ 2 , 3 , 5 , 7 , 10 ] as basic references on the subject.

[Partial differential equations] [L. C. Evans]是数学系 偏微分方程专业的基础课之一，需要好好学习

SUMS18 Numerical Methods for Partial Differential Equations, Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley (2000) .zip

Finite Difference Schemes and Partial Differential Equations

Lions-Generalized_Solutions_of_Hamilton-Jacobi_Equations.djvu

Evans-Entropy and partial differential equations. Evans 版偏微分方程补充内容