The course is conducted in Chinese but uses English textbook。Intensive courses。

This half-semester course contains two main topics, which are vector Calculus and Taylor series. Vector Calculus deals with functions whose domain and range are both in R^n, which are called vector fields. We will make sense of integrating vector fields over curves and surfaces and introduce two differential operators acting on them, the divergence and curl. We will explain how Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem connect the integration and differentiation of vector fields and are regarded as higher-dimensional Fundamental Theorem of Calculus. As an application, we will derive Gauss' Law in electromagnetism, which describes the flux of an inverse square field across a closed surface. The topic of the Taylor series extends the concept of limit to approximating complicated functions by polynomials. We will introduce the convergence of series and power series, use Taylor’s Theorem to estimate remainder terms and derive Taylor series for common functions. Finally, applications of approximating functions by polynomials are illustrated. Definitions are discussed, and the most important theorems are derived in the lectures with a view to helping students develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sections in which students are able to improve their skills in handling calculations in Calculus and complete small projects under the guidance of our teaching assistants.

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis, and Differential Equations.

Before taking this course, students should be already skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test which is designed for NTU freshmen. Students are expected to attend and participate actively in lectures as well as discussion sessions.

Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition.  其他相關資訊 微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
 台大微積分考古題:  http://www.math.ntu.edu.tw/~calc/cl_n_34455.html
 數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal 
 免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator  免費知識型計算引擎: https://www.wolframalpha.com