Advanced calculus I-1

Advanced calculus plays a pivotal role in the realm of mathematics education, serving as the bridge that connects elementary numerical computations to the more intricate world of advanced abstract thinking. It is a subject that often instills trepidation in students as they begin their journey into its complexities. The pages that follow are a product of the author's extensive experience in teaching advanced calculus courses at the mathematics department of National Tsinghua University of Taiwan. The primary objective of these books is to provide mathematics textbooks optimized for mobile phone readability, complete with vibrant visuals to enhance the learning experience. Within these pages, every proof is presented with simplicity in mind, making them accessible, comprehensive, and enriched with graphics and colors. The author's aspiration is to foster greater receptiveness among students, encouraging them to invest more time in this essential course.

Advanced calculus is a rigorous two-semester course, bearing the weight of four credits per semester, with 200 minutes of instruction weekly, accompanied by two hours of recitation, weekly assignments, and four exams per semester. It stands as one of the most challenging classes in the mathematics department, demanding a substantial commitment from students. In the modern era, proficiency in mathematics and abstract thinking is becoming increasingly critical in scientific and technological fields. Mathematics is intrinsically linked to automated processes and big data analysis, making it an indispensable skill. This is why this demanding course continues to attract students from diverse disciplines, including electrical engineering, computer science, financial engineering, management, and medical school.

To cater to the needs of mobile phone users, the book files are designed to be manageable in size. As a result, the content of Advanced Calculus I is divided into two volumes, each aligned with specific exam content: Advanced Calculus I-1 and Advanced Calculus I-2, each encompassing two exams. All exams and practice tests are thoughtfully included within the books, with exercises accompanying each section. Despite being written in English, the language used is intentionally not overly complex. Building upon foundational calculus knowledge, these textbooks can be regarded as self-contained and suitable for self-study.