The course is conducted in English。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 that describes the flux of an inverse square field across a closed surface. The topic of 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 help students to 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. 課程資訊請參考統一教學網: http://www.math.ntu.edu.tw/~calc/Default.html See the Calculus website for general info: http://www.math.ntu.edu.tw/~calc/Default.html

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.

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