麻省理工开放课程：多变量微积分 Multivariable Calculus 共35课更新完毕[MP4]

游客，本帖隐藏的内容需要积分高于 1 才可浏览，您当前积分为 0

资源信息： 中文名: 麻省理工开放课程：多变量微积分 英文名: Multivariable Calculus 资源格式: MP4 课程类型: 数学 学校: 麻省理工 MIT 主讲人: Prof. Denis Auroux 版本: 共35课更新完毕 发行日期: 2007年 地区: 美国 对白语言: 英语 概述:

课程介绍： 本课程内容包括向量和多变量微积分,属于是一年级第二学期微积分课程。 主题包括向量和矩阵，偏导数，双重和三重积分，平面和空间微积分。 麻省理工学院开放式课程提供了另外2006年春季的18.02版本。 这两个版本使用相同的内容，他们是由不同的教师授课，并依赖于不同的教科书。 多变量微积分（18.02）是麻省理工学院秋季和春季的任教课程，是麻省理工学院所有本科生必修科目。 导师介绍

Denis Auroux received the Maîtrice in mathematics from the École Normale Supérieure, Paris VII in 1994, the Licence in physics from Paris VI in 1995, the Diploma in mathematics from the Université de Paris Sud, 1995, and the Ph.D. from École Polytechnique in 1999. Jean-Pierre Bourguignon and Misha Gromov were his doctoral advisors. He completed the habilitation at the University of Paris Sud in 2003. He came to MIT as a CLE Moore instructor in 1999 and joined the MIT mathematics faculty in 2002. He was promoted to associate professor in 2004 and tenured in 2006. Professor Auroux's research interests are in the fields of symplectic topology and mirror symmetry. His distinctions include the Prix de Thèse, École Polytechnique, 1999; the Prix Peccot & Cours Peccot, Collège de France, January 2002, and the Alfred P. Sloan Research Fellowship, 2005. He received the MIT School of Science Prize for Excellence in Undergraduate Teaching in 2006. 截图：

注： 1.我会把麻省所有的微积分课程发出来，大约200个视频，有需要的同学请关注。 2.课件：http://ocw.mit.edu/courses/mathematics/18-...terials/，因为官网速度下载较快，这里暂不提供。 3.个人翻译的标题,有啥错误还请慷慨指正. 目录: Lecture 01: Dot product Lecture 02: Determinants; cross product Lecture 03: Matrices; inverse matrices Lecture 04: Square systems; equations of planes Lecture 05: Parametric equations for lines and curves Lecture 06: Velocity, acceleration; Kepler's second law Lecture 07: Review Lecture 08: Level curves; partial derivatives; tangent plane approximation Lecture 09: Max-min problems; least squares Lecture 10: Second derivative test; boundaries and infinity Lecture 11: Differentials; chain rule Lecture 12: Gradient; directional derivative; tangent plane Lecture 13: Lagrange multipliers Lecture 14: Non-independent variables Lecture 15: Partial differential equations; review Lecture 16: Double integrals 47:59 Denis Auroux Lecture 17: Double integrals in polar coordinates; applications Lecture 18: Change of variables Lecture 19: Vector fields and line integrals in the plane Lecture 20: Path independence and conservative fields Lecture 21: Gradient fields and potential functions Lecture 22: Green's theorem Lecture 23: Flux; normal form of Green's theorem Lecture 24: Simply connected regions; review Lecture 25: Triple integrals in rectangular and cylindrical coordinates Lecture 26: Spherical coordinates; surface area Lecture 27: Vector fields in 3D; surface integrals and flux Lecture 28: Divergence theorem Lecture 29: Divergence theorem (cont.): applications and proof Lecture 30: Line integrals in space, curl, exactness and potentials Lecture 31: Stokes' theorem Lecture 32: Stokes' theorem (cont.); review Lecture 33: Topological considerations; Maxwell's equations Lecture 34: Final review Lecture 35: Final review (cont.)