Advanced Mathematics Concise Tutorial, Second Edition

Author: Li Zhong
Publisher:
Publish Date: 1999-01-01
Features: This textbook is a higher education teaching material for university students majoring in physics, divided into three volumes for three semesters. The first volume covers calculus of single-variable functions and spatial analytical geometry; the second volume covers calculus of multivariable functions and ordinary differential equations; the third volume covers series, integral with parameter, Fourier series and Fourier integral, probability theory and mathematical statistics. This book is the second volume, divided into four chapters. The content includes: differential calculus of multivariable functions and its applications in geometry, double integrals, triple integrals and their applications in physics, line integrals, surface integrals, and an introduction to field theory, as well as ordinary differential equations. The authors of this book have been officially approved by the Beijing Municipal Education Commission and Peking University to carry out pilot work on the reform of the content system of higher mathematics courses. This book was written based on the pilot program. It breaks the traditional teaching order of first discussing differential calculus and then integral calculus, and restructures the teaching content system, aiming to help readers quickly grasp the core ideas and basic calculations of calculus. At the same time, it avoids the disconnection with other foundational courses caused by the late introduction of integral concepts. In the treatment of limit theory and related issues, this book has distinctive features, ensuring the rigor of theory while avoiding excessive formalism, making the content feel natural and intuitive to readers. This book emphasizes the practical background of mathematical theory and its role in other disciplines. The presentation of content, as well as the arrangement of exercises and examples, highlights the application value of mathematics. The book is concise, easy to understand, and suitable for self-study. It can be used as a textbook for higher mathematics courses for physics majors and related disciplines in comprehensive universities and normal universities. It can also be read by mathematics teachers, scientific and technological workers, and mathematics enthusiasts. For non-physics majors, it can also be selectively used as a higher mathematics textbook.