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دسته بندی: تحلیل و بررسی ویرایش: نویسندگان: Bourchtein. Andrei, Bourchtein. Ludmila سری: Textbooks in mathematics (Boca Raton Fla.) ISBN (شابک) : 9781482246674, 1482246678 ناشر: CRC Press سال نشر: 2014 تعداد صفحات: 358 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 5 مگابایت
کلمات کلیدی مربوط به کتاب CounterExamples: از حساب ابتدایی تا آغاز تجزیه و تحلیل: ریاضیات، حساب دیفرانسیل و انتگرال
در صورت تبدیل فایل کتاب CounterExamples: From Elementary Calculus to the Beginnings of Analysis به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب CounterExamples: از حساب ابتدایی تا آغاز تجزیه و تحلیل نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
"In this
manuscript we present counterexamples to different false
statements, which frequently arise in the calculus and
fundamentals of real analysis, and which may appear to be
true at first glance. A counterexample is understood here in
a broad sense as any example that is counter to some
statement. The topics covered concern functions of real
variables. The first part (chapters 1-6) is related to
single-variable functions, starting with elementary
properties of functions (partially studied even in college),
passing through limits and continuity to differentiation and
integration, and ending with numerical sequences and series.
The second part (chapters 7-9) deals with function of two
variables, involving limits and continuity, differentiation
and integration. One of the goals of this book is to provide
an outlook of important concepts and theorems in calculus and
analysis by using counterexamples.We restricted our
exposition to the main definitions and theorems of calculus
in order to explore different versions (wrong and correct) of
the fundamental concepts and to see what happens a few steps
outside of the traditional formulations. Hence, many
interesting (but more specific and applied) problems not
related directly to the basic notions and results are left
out of the scope of this manuscript. The selection and
exposition of the material are directed, in the first place,
to those calculus students who are interested in a deeper
understanding and broader knowledge of the topics of
calculus. We think the presented material may also be used by
instructors that wish to go through the examples (or their
variations) in class or assign them as homework or
extra-curricular projects. In order to make the majority of
the examples and solutions accessible to"--
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more...
Abstract: "This book provides a one-semester undergraduate
introduction to counterexamples in calculus and analysis. It
helps engineering, natural sciences, and mathematics students
tackle commonly made erroneous conjectures. The book
encourages students to think critically and analytically, and
helps to reveal common errors in many examples.In this book,
the authors present an overview of important concepts and
results in calculus and real analysis by considering false
statements, which may appear to be true at first glance. The
book covers topics concerning the functions of real
variables, starting with elementary properties, moving to
limits and continuity, and then to differentiation and
integration. The first part of the book describes
single-variable functions, while the second part covers the
functions of two variables.The many examples presented
throughout the book typically start at a very basic level and
become more complex during the development of exposition. At
the end of each chapter, supplementary exercises of different
levels of complexity are provided, the most difficult of them
with a hint to the solution.This book is intended for
students who are interested in developing a deeper
understanding of the topics of calculus. The gathered
counterexamples may also be used by calculus instructors in
their classes. "--
"In this manuscript we present counterexamples to different false statements, which frequently arise in the calculus and fundamentals of real analysis, and which may appear to be true at first glance. A counterexample is understood here in a broad sense as any example that is counter to some statement. The topics covered concern functions of real variables. The first part (chapters 1-6) is related to single-variable functions, starting with elementary properties of functions (partially studied even in college), passing through limits and continuity to differentiation and integration, and ending with numerical sequences and series. The second part (chapters 7-9) deals with function of two variables, involving limits and continuity, differentiation and integration. One of the goals of this book is to provide an outlook of important concepts and theorems in calculus and analysis by using counterexamples.We restricted our exposition to the main definitions and theorems of calculus in order to explore different versions (wrong and correct) of the fundamental concepts and to see what happens a few steps outside of the traditional formulations. Hence, many interesting (but more specific and applied) problems not related directly to the basic notions and results are left out of the scope of this manuscript. The selection and exposition of the material are directed, in the first place, to those calculus students who are interested in a deeper understanding and broader knowledge of the topics of calculus. We think the presented material may also be used by instructors that wish to go through the examples (or their variations) in class or assign them as homework or extra-curricular projects. In order to make the majority of the examples and solutions accessible to"
Content: Introduction Comments On the structure of this book On mathematical language and notation Background (elements of theory) Sets Functions FUNCTIONS OF ONE REAL VARIABLE Elementary properties of functions Elements of theory Function definition Boundedness Periodicity Even/odd functions Monotonicity Extrema Exercises Limits Elements of theory Concepts Elementary properties (arithmetic and comparative) Exercises Continuity Elements of theory Local properties Global properties: general results Global properties: the famous theorems Mapping sets Weierstrass theorems Intermediate Value theorem Uniform continuity Exercises Differentiation Elements of theory Concepts Local properties Global properties Applications Tangent line Monotonicity and local extrema Convexity and inflection Asymptotes L'Hospital's rule Exercises Integrals Elements of theory Indefinite integral Definite (Riemann) integral Improper integrals Applications Exercises Sequences and series Elements of theory Numerical sequences Numerical series: convergence and elementary properties Numerical series: convergence tests Power series Exercises FUNCTIONS OF TWO REAL VARIABLES Limits and continuity Elements of theory One-dimensional links Concepts and local properties Global properties Multidimensional essentials Exercises Differentiability Elements of Theory One-dimensional links Concepts and local properties Global properties and applications Multidimensional essentials Exercises Integrability Elements of theory One-dimensional links Multidimensional essentials Exercises Bibliography Symbol Description Index