Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or appl...
Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features of Basic Real Analysis
* Early chapters treat...
Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure ...
Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features of Advanced Real Analysis
* Develops Fourier...
Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pu...
This is a revised and extended version of my 1995 elementary introduction to partial di?erential equations. The material is essentially the same except for three new chapters. The ?rst (Chapter 8) is about non-linear equations of ?rst order and in particular Hamilton-Jacobi equations. It builds on the continuing idea that PDEs, although a branch of mathematical analysis, are closely related to models of physical phenomena. Such underlying physics in turn provides ideas of solvability. The Hopf variational approach to the Cauchy problem for Hamilton-Jacobi equations is one of the clearest and...
This is a revised and extended version of my 1995 elementary introduction to partial di?erential equations. The material is essentially the same excep...
I am sure that something must be found. There must exist a notion of generalized functions which are to functions what the real numbers are to the rationals (G. Peano, 1912) Not that much effort is needed, for it is such a smooth and simple theory (F. Treves, 1975) In undergraduate physics a lecturer will be tempted to say on certain occasions: "Let ?. x/ be a function on the line that equals 0 away from 0 and is in?nite at 0 in such a way that its total integral is 1. The most important property of ?. x/ is exempli?ed Z by the identity 1 . x/?. x/ dx D . 0/; 1 where is any continuous...
I am sure that something must be found. There must exist a notion of generalized functions which are to functions what the real numbers are to the rat...
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $ar$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces. The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course.
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $ar$-method...
Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's results. The concept of orthogonality weaves the material into a coherent whole. This textbook will...
Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from un...
Culture is something we build, something we do with creation; it is the outward expression of a people’s worship, in terms of which they cultivate their society, including its law, education, arts and customs and much more besides. Whether we realize it or not, we all participate daily in culture-building of one form or another. The gospel of the kingdom is the good news that Jesus Christ is King of kings and Lord of lords, and that he is at work to redeem this fallen world, remaking it in accordance with his good purposes. To speak of gospel culture, then, is to...
Culture is something we build, something we do with creation; it is the outward expression of a people’s worship, in terms of which ...
