First step in advanced mathematics

Author: Gong Chengtong
Publisher:
Publish Date: 2004-07-01
Features: This book is designed as a teaching aid for first-year university students, addressing the gaps often found between secondary school mathematics education and university-level mathematics. The main content includes: parametric equations, polar coordinates, translation and rotation of coordinates, partial fraction decomposition of rational functions, determinants, Euler's formula for complex numbers, and topics on arbitraryness, existence, and uniqueness (primarily focusing on amplification and reduction principles for proving the existence of solutions to inequalities), finite and infinite, counterexamples and proof by contradiction, etc. All these topics are either superficially covered or entirely absent in secondary school mathematics but are crucial in university mathematics. To enable readers to learn as much as possible in the least amount of time, the book provides detailed explanations for each section, (meticulously drawn illustrations), and includes a sufficient number of exercises with solutions or hints at the end of each chapter to help readers understand and reinforce the material. This book serves as a ladder for climbing from secondary school mathematics to university mathematics and a springboard for students starting their university mathematics journey. It is suitable as a reference book for students of various higher education institutions (including full-time universities, radio and television universities, vocational colleges, part-time universities, adult education institutions, and private universities), covering all undergraduate and junior college majors (such as science and engineering, economics, management, medical and agricultural, liberal arts and law, and mathematics). It can also be used as a teaching material for extracurricular tutoring by university mathematics teachers and secondary school mathematics teachers.