SPOC学校专有课程
Calculus II (微积分II)
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spContent=源自欧美教学风格,采用原版经典英文教材《Thomas' Calculus》(第13版),全英文授课方式,给学习者带来不一样的微积分学习体验,有兴趣的同学来挑战吧!Welcome!
—— 课程团队
课程概述

    微积分课程是理、工、管理等大学本科专业最重要的数学基础课程,为学生学习后续课程和进一步获取数学知识尊定基础,也是培养学生理性思维和创新能力的重要载体。

      2013年秋至今,电子科技大学为了格拉斯哥学院学生的教学与培养需要,开设了全英语微积分课程,选用的教材是英语原版经典教材《ThomasCalculus》(第13版)。授课方式为全英语教学,并按照欧美教学方式:注重以学生为中心、课内与课外相结合、教学与研究相结合、知识背景与理论基础相结合的教育创新模式。教师在课程中积极与学生互动,注重学生发现问题、解决问题能力的培养,同时讲解问题时留有充分的想象空间与练习环节,并附有丰富的参考资料和大量的例题习题。

      本课程系统地介绍了微积分的基础知识和基本方法,分为Calculus ICalculus II两个部分。Calculus I主要包含一元函数的极限理论,一元函数微分学和积分学,常微分方程;Calculus II主要包含多元函数微分学与积分学,向量场积分以及无穷级数理论。

授课目标

By the end of this course students will be able to:

·       apply calculus to parametric functions and vector-valued functions;

·       understand the inner and cross products of vectors, and apply them to lines and planes in space;

·       introduce the polar coordinates and the related equations;

·       calculate partial derivatives, total differential and high-order partial derivatives of multivariable functions;

·       find the derivative of implicit functions;

·       explain the concepts of directional derivative and gradient and calculate them in two and three dimensions;

·       apply partial derivatives to find the tangent plane and normal line of a surface;

·       locate extreme values of a multivariable function, both unconstrained and under given conditions, and apply the Lagrange multiplier method;

·       describe the meaning of double integrals (Cartesian coordinates and Polar coordinates) and evaluate them; similarly for triple integral (Cartesian coordinates, Polar coordinates and Spherical coordinates);

·       evaluate open and closed line integrals of vector functions, aware that the results depends on the path in general;

·       deetermine whether a line integral is independent of path;

·       apply Green’s theorem to integrals in the plane;

·       express given surfaces in an appropriate form and evaluate surface integrals over both open and closed surfaces;

·       apply the theorems of Green, Gauss and Stokes to line, surface and volume integrals and explain their significance in engineering;

·       explain what is meant by conservative, irrotational and solenoidal fields and explain their physical meaning

·       state what is meant by a sequence and series, find limits of sequence;

·       apply criteria for convergence of series with terms of the same sign or alternating sign; distinguish between absolute convergence and conditional convergence;

·       establish conditions for convergence of power series, other functional series and Taylor series;

·       derive Maclaurin expansions of elementary transcedental functions such as sin(x) and cos(x);

·       apply direct and indirect expansion methods of some simple functions to applications of power series in approximate calculations.

成绩 要求

课程成绩评定由两部分构成:

(1)单元测验:在每一章学习结束后有一次单元测验,所有单元测验分数占课程总成绩的40%。

(2)课程考试:课程结束后,学生可以参加课程的最后考试,考试成绩占总成绩的60%。

完成课程学习并考核合格(>=60分)的可获得合格证书,成绩优秀(>=85分)的可获得优秀证书。


课程大纲
预备知识

Calculus I