Vector Calculus

新的版本，除了符合應用工程學上，新的需求之外，筆者還特別精挑細選，補充了一些例題、習題以及應用題。重新編訂後的版本，筆者將其命名為《Vector Calculus with its Applications (向量演算學及其應用)》，無論是在字體或是符號上而言，都有新的面貌。

This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as

This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed a

Table of Contents:Chapter 0 PrecalculusChapter 1 Functions and LimitsChapter 2 DerivativesChapter 3 Inverse FunctionsChapter 4 Applications of DerivativesChapter 5 IntegralsChapter 6 Techniques of IntegrationChapter 7 Applications of IntegrationChapter 8 Parametric Equations and Polar CoordinatesChapter 9 Vector SpacesChapter 10 Partial DerivativesChapter 11 Multiple IntegralsChapter 12 Sequences and SeriesAppendix A The Precise Definition of LimitsAppendix B Change of VariablesAppendix C Vector CalculusExercise AnswersIndex

●Introduces central topics, such as vector spaces, linear maps, linear dependence, and eigenvalues, early in the book with the aim of helping students transition from calculus to rigorous mathematics●

This book provides a general introduction to applied analysis, vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, i

How to define the vector division has been plagued by people. We redefine the fraction , where represents an arbitrary vector, and extend it to discuss the differentiability and integrability of two or more variables function. In this book we directly exploit the definition of derivatives for two variable functions. According to our research, we discover various forms of the Mean Value(Vector) Theorems and the Fundamental Theorems of Calculus for multiple integrals. This book adds a new understanding to the field of multi-variable calculus and thus helps those who are working in the subject.We divide our research into three sections in this book. In Chapter 1, by defining the line derivector and plane derivector, we explain the chain rule for differentiation of multi-variables function, differential and the mean vector theorem. In Chapter 2, we illustrate the formula derivation of i) line derivector for a 2-variable function, ii) line derivatives for 2-variable functi