Advanced Calculus (English Version) (English Version)

Author: Patrick Fitzpatrick
Publisher:
Publish Date: 2003-05-01
Features: Mathematical analysis has become firmly established in all branches of natural and social sciences. As the foundation of mathematical analysis, calculus not only provides methodology for all mathematical methods and algorithmic tools but also instills logical thinking methods in people. This book has achieved remarkable results in achieving this goal, allowing readers not only to gain knowledge of calculus but also to be trained in mathematical scientific thinking. It is suitable as a textbook for undergraduate and graduate students in science and engineering disciplines with a certain foundation in mathematical analysis. Mathematical analysis has become firmly established in all branches of natural and social sciences. As the foundation of mathematical analysis, calculus not only provides methodology for all mathematical methods and algorithmic tools but also instills logical thinking methods in people. This book has achieved remarkable results in achieving this goal, allowing readers not only to gain knowledge of calculus but also to be trained in mathematical scientific thinking. It is suitable as a textbook for undergraduate and graduate students in science and engineering disciplines with a certain foundation in mathematical analysis. The entire book can be taught over two semesters. Features of the book:
■ On one hand, the book introduces all topics of calculus in a traditional and rigorous deductive form, while on the other hand, it emphasizes the relevance and unity of the topics, organizing the material from a holistic and systematic perspective.
■ Part of the book covers the calculus of single-variable functions, including real numbers, the convergence of sequences, the continuity and limits of functions, the derivatives and integrals of functions, and polynomial approximations. The second part extends the concept of multiple integrals to multidimensional Euclidean space and discusses the partial derivatives of multivariable functions, inverse functions, implicit functions and their applications, line integrals, and surface integrals.
■ A dedicated chapter is devoted to metric spaces, where many concepts and derived results introduced in calculus in Euclidean space can be discussed in this more abstract space.
■ The book includes numerous exercises of moderate difficulty.