Karel Hrbacek, Olivier Lessmann, Richard O'Donovan

"This book presents an alternative approach to differential and integral calculus of functions of one variable. … For readers familiar with the classical methods of mathematical analysis, this book can provide an interesting alternative view."—Zentralblatt MATH 1317"What the book does exceptionally well is explain and develop the basic notions and machinery slowly, invitingly, methodically, and enjoyably. … Numerous solved exercises make the book highly efficient in learning the nonstandard technique it advocates but also for learning the elements of calculus … the book is a well-aimed stab at the heart of the teaching of analysis and presents a very interesting nonstandard approach. Any student intrigued by the subject of nonstandard analysis will find the book to be entertaining and well-written, and to present a coherent approach at a very elementary level."—MAA Reviews, March 2015

• ELEMENTARY ANALYSIS: Basic Concepts. Continuity and Limits. Differentiability. Elementary Integration. HIGHER ANALYSIS: Basic Concepts Revisited. Derivatives. Sequences and Series. Topology of Real Numbers. Differential Equations. Integration. Appendix. Index.

Karel Hrbacek, Olivier Lessmann, Richard O'Donovan

"This book presents an alternative approach to differential and integral calculus of functions of one variable. … For readers familiar with the classical methods of mathematical analysis, this book can provide an interesting alternative view."—Zentralblatt MATH 1317"What the book does exceptionally well is explain and develop the basic notions and machinery slowly, invitingly, methodically, and enjoyably. … Numerous solved exercises make the book highly efficient in learning the nonstandard technique it advocates but also for learning the elements of calculus … the book is a well-aimed stab at the heart of the teaching of analysis and presents a very interesting nonstandard approach. Any student intrigued by the subject of nonstandard analysis will find the book to be entertaining and well-written, and to present a coherent approach at a very elementary level."—MAA Reviews, March 2015

• ELEMENTARY ANALYSIS: Basic Concepts. Continuity and Limits. Differentiability. Elementary Integration. HIGHER ANALYSIS: Basic Concepts Revisited. Derivatives. Sequences and Series. Topology of Real Numbers. Differential Equations. Integration. Appendix. Index.