Showing top programs at National Taiwan University. To view all programs, visit the official site →
Showing top programs at National Taiwan University. To view all programs, visit the official site →
This course delves into the fundamental concepts of Calculus, exploring the relationship between numbers and shapes that is central to mathematics. It covers the historical development of calculus from ancient practical needs to its formalization by Newton and Leibniz, and its subsequent applications in various scientific fields. The course aims to provide a comprehensive understanding of calculus as the study of continuous quantities, emphasizing its logical foundation and connection to intuitive ideas. It addresses key areas such as sequences and series convergence, the behavior of functions, and the rigorous definitions of limits and continuity. The curriculum is designed to build a solid logical basis for mathematical analysis, enabling students to grasp complex mathematical objects and concepts through a constructive approach. Compared to introductory calculus courses that focus more on intuitive geometric and algebraic reasoning, this course emphasizes clarifying the crucial points often bypassed in simpler treatments. It bridges the gap between rigorous logical methods and intuitive understanding, while still including practical examples and problem-solving.
