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Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)

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Review From the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."―MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a fullblown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common misproof fails." ―Allen Stenger (The Mathematical Association of America, June, 2008) Read more From the Back Cover For over three decades, this bestselling classic has been used by thousands of students in the United States and abroad as a musthave textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of wellchosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, wellmotivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowheredifferentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."―MATHEMATICAL REVIEWS Read more See all Editorial Reviews
Review From the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."―MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a fullblown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common misproof fails." ―Allen Stenger (The Mathematical Association of America, June, 2008) Read more From the Back Cover For over three decades, this bestselling classic has been used by thousands of students in the United States and abroad as a musthave textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of wellchosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, wellmotivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowheredifferentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."―MATHEMATICAL REVIEWS Read more See all Editorial Reviews
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Review From the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."―MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a fullblown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common misproof fails." ―Allen Stenger (The Mathematical Association of America, June, 2008) Read more From the Back Cover For over three decades, this bestselling classic has been used by thousands of students in the United States and abroad as a musthave textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of wellchosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, wellmotivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowheredifferentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."―MATHEMATICAL REVIEWS Read more See all Editorial Reviews
Review From the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."―MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a fullblown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common misproof fails." ―Allen Stenger (The Mathematical Association of America, June, 2008) Read more From the Back Cover For over three decades, this bestselling classic has been used by thousands of students in the United States and abroad as a musthave textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of wellchosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, wellmotivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowheredifferentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."―MATHEMATICAL REVIEWS Read more See all Editorial Reviews
20190610 11:22:48

