中文摘要：

从计算一阶和二阶各种导数形式的角度，讨论了自动微分的基本原理和方法，给出了一阶和二阶各种微分模式最简单而最直观的表述形式，分别讨论了用不同微分模式计算不同导数形式的计算代价，讨论并给出了非线性问题求解中常用数值算法的计算代价．讨论了断点存储、正向积分和反向积分方法．

英文摘要：

We study fundamentals and techniques of automatic differentiation by discussing the way for calculating different kinds of first- and second-order derivatives. First we present the first- and second-order differentiation models in a simple way, then discuss the costs in terms of operations count and memory for calculating different derivatives with different differen- tiation models, finally discuss some typical algorithms in solving the nonlinear problems via automatic differentiation with respect to the computational costs, both in operations count and in memory. Several fundamental techniques including checkpointing, forward accumulating and backward accumulating are discussed.