Using minimal prerequisites, this book unlocks the power Lebesgue integral, accessible at a surprisingly early stage in the undergraduate curriculum.
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William Johnston is Professor of Mathematics at Butler University, Indiana. His publications include articles on operator theory and functional analysis, and the undergraduate textbooks A Transition to Advanced Mathematics: A Survey Course (with Alex McAllister) and An Introduction to Statistical Inference.
In 1902, modern function theory began when Henri Lebesgue described a new “integral calculus.” His “Lebesgue integral” handles more functions than the traditional integral–so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.
In 1902, modern function theory began when Henri Lebesgue described a new integral calculus. His Lebesgue integral handles more functions than the traditional integral so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.
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Hardback. Condizione: New. This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single- variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text.s use of a method labeled the .Daniell-Riesz approach. The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist. Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions. Codice articolo LU-9781939512079
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Condizione: New. Using minimal prerequisites, this book unlocks the power Lebesgue integral, accessible at a surprisingly early stage in the undergraduate curriculum. Series: Mathematical Association of America Textbooks. Num Pages: 200 pages. BIC Classification: PBKL. Category: (U) Tertiary Education (US: College). Dimension: 253 x 177. . . 2015. Hardcover. . . . . Codice articolo V9781939512079
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Condizione: New. Using minimal prerequisites, this book unlocks the power Lebesgue integral, accessible at a surprisingly early stage in the undergraduate curriculum. Series: Mathematical Association of America Textbooks. Num Pages: 200 pages. BIC Classification: PBKL. Category: (U) Tertiary Education (US: College). Dimension: 253 x 177. . . 2015. Hardcover. . . . . Books ship from the US and Ireland. Codice articolo V9781939512079
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