Introduction to Calculus and Mathematical Analysis. Volume 2, Part 1

Author: Frank J. Flyod
Publisher:
Publish Date: 2001-03-01
Features: This book systematically elaborates on the fundamental theories of calculus. In the presentation, the author strives to achieve both rigor and accessibility, highlighting the intrinsic connections between concepts and their intuitive background. The original book is divided into two volumes: Volume I covers single-variable cases, while Volume II deals with multivariable cases. The Chinese translation of Volume II is published in two parts. This book is the second part of Volume II, including Chapters 1-3. Chapter 1 provides an in-depth discussion of multivariable functions and their derivatives, including linear differential forms and their integrals, supplemented by rigorous proofs of fundamental concepts in mathematical analysis. Chapter 2 prepares sufficient material for modern mathematical analysis in terms of linear algebra. Chapter 3 narrates the development and applications of multivariable differential calculus, including rigorous proofs of the implicit function theorem, the basic theory of multivariable transformations and mappings, differential geometry fundamentals of curves and surfaces, and fundamental concepts of exterior differential forms. The original book includes exercise solutions, which are compiled into each part. This book is the second part of Volume II, including Chapters 4-8. Chapter 4 introduces multiple integrals; Chapter 5 discusses the relationship between surface integrals and volume integrals; Chapter 6 covers differential equations; Chapter 7 introduces the calculus of variations; and Chapter 8 discusses single-valued and multiple-valued complex functions. Each chapter includes examples, exercises, and solutions, supplemented by appendices introducing related content. The target audience is faculty and students in science and engineering disciplines at universities and colleges, as well as engineering professionals.