麻省理工学院「开放式课程网页」 | 数学 | 18.024 2003春季课程：微积分及理论II

微积分理论包括两部分：18.014和18.024。本课程是第二部分，教学采用T. Apostol编写的《微积分》第二版(1967)卷I卷II，以及退休数学教授James Raymond Munkres编写的课程讲稿。本网站提供作业，复习/实习课程及课程笔记。

This is the second course in a two-part sequence on Calculus with Theory, 18.014 and 18.024. The course is taught using the textbook by T. Apostol, Calculus, Vols. I and II, Second Edition (1967), and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus. The website features problem sets, recitation assignments, and course notes.

本课程是18.014的后续课程，它包括和课程18.02(微积分)相同的材料，但程度更深，强调严谨的推理和对证明的理解，对线性代数和向量积分也有相当的强调。

主题包括: 多元微积分，三维空间中的向量代数、行列式、矩阵，一元向量值函数、空间运动，多元标量函数；偏微分、梯度、优化技巧，平面上的双重积分和线积分；正合微分和保守场；格林定理及其应用、三重积分、空间中的线积分和面积分、散度定理、斯托克斯定理；应用。

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.

Lachowska博士感谢Andrew Brooke-Taylor和Alex Retakh对本课程网站的帮助。
Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor and Alex Retakh for their help with this course web site.