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《Thomas' Calculus》（第12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 I和Calculus 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。

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.

Calculus I

《Thomas' Calculus》, G. B. Thomas, M. D. Weir and J. R. Hass, 12th edition, Pearson's company, 2010: https://www.mypearsonstore.com/bookstore/thomas-calculus-9780321587992