The purpose of this book is to assist students in completing basic training in elementary mathematics, enabling them to smoothly begin and successfully complete the study of advanced mathematics such as calculus. We firmly believe that once students have mastered fundamental algebraic concepts and operational skills, learned geometry, trigonometric functions, and other elementary functions in mathematics, they can further study numbers, functions, geometric shapes, and related practical problems from both a microscopic perspective (the viewpoint of limits and differentials) and a macroscopic perspective (the viewpoint of limits and integrals). In the end, the majority of them will successfully and timely complete their university education.