Advanced Calculus A Transition to Analysis

Author: CTI Reviews
Publisher: Cram101 Textbook Reviews
ISBN: 1490297731
Format: PDF, ePub
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Facts101 is your complete guide to Advanced Calculus, A Transition to Analysis. In this book, you will learn topics such as plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Advanced Calculus

Author: Leonard F. Richardson
Publisher: John Wiley & Sons
ISBN: 1118030672
Format: PDF
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Features an introduction to advanced calculus and highlights itsinherent concepts from linear algebra Advanced Calculus reflects the unifying role of linearalgebra in an effort to smooth readers' transition to advancedmathematics. The book fosters the development of completetheorem-proving skills through abundant exercises while alsopromoting a sound approach to the study. The traditional theoremsof elementary differential and integral calculus are rigorouslyestablished, presenting the foundations of calculus in a way thatreorients thinking toward modern analysis. Following an introduction dedicated to writing proofs, the bookis divided into three parts: Part One explores foundational one-variable calculus topics fromthe viewpoint of linear spaces, norms, completeness, and linearfunctionals. Part Two covers Fourier series and Stieltjes integration, whichare advanced one-variable topics. Part Three is dedicated to multivariable advanced calculus,including inverse and implicit function theorems and Jacobiantheorems for multiple integrals. Numerous exercises guide readers through the creation of theirown proofs, and they also put newly learned methods into practice.In addition, a "Test Yourself" section at the end of each chapterconsists of short questions that reinforce the understanding ofbasic concepts and theorems. The answers to these questions andother selected exercises can be found at the end of the book alongwith an appendix that outlines key terms and symbols from settheory. Guiding readers from the study of the topology of the real lineto the beginning theorems and concepts of graduate analysis,Advanced Calculus is an ideal text for courses in advancedcalculus and introductory analysis at the upper-undergraduate andbeginning-graduate levels. It also serves as a valuable referencefor engineers, scientists, and mathematicians.

Analysis

Author: Steven R. Lay
Publisher:
ISBN: 9780130898791
Format: PDF
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For courses in Real Analysis, Advanced Calculus, and Transition to Advanced Mathematics or Proofs course. Carefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps students in the transition from computationally oriented courses to abstract mathematics by its emphasis on proofs. Student oriented and instructor friendly, it features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected exercises. *NEW - True/False questions - (More than 250 total) located at the beginning of the exercises for each section and relating directly to the reading. *NEW - 8 new illustrations of key concepts make this the most visually compelling analysis text. *Straightforward discussion of logic - As it applies to the proving of theorems in analysis (Ch. 1). Can be covered briefly or in depth, depending on the needs of students. *Practice problems - Scattered throughout the narrative (more than 140 total). These problems relate directly to what has just been presented. Includes complete answers at the end of each section. *Fill-in-the-blank proofs. Helps stude

Problems in Real Analysis

Author: Teodora-Liliana Radulescu
Publisher: Springer Science & Business Media
ISBN: 0387773789
Format: PDF, ePub, Docs
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Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Introduction to Calculus and Classical Analysis

Author: Omar Hijab
Publisher: Springer Science & Business Media
ISBN: 0387693165
Format: PDF, Mobi
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Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

A Concise Approach to Mathematical Analysis

Author: Mangatiana A. Robdera
Publisher: Springer Science & Business Media
ISBN: 0857293478
Format: PDF, Kindle
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This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.

Real Analysis

Author: Saul Stahl
Publisher: John Wiley & Sons
ISBN: 9780471318521
Format: PDF, ePub
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A provocative look at the tools and history of real analysis This new work from award-winning author Saul Stahl offers a real treat for students of analysis. Combining historical coverage with a superb introductory treatment, Real Analysis: A Historical Approach helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn-illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, introducing the various aspects of the completeness of the real number system, sequential continuity and differentiability, as well as uniform convergence. Finally, he presents applications and examples to reinforce concepts and demonstrate the validity of many of the historical methods and results. Ample exercises, illustrations, and appended excerpts from the original historical works complete this focused, unconventional, highly interesting book. It is an invaluable resource for mathematicians and educators seeking to gain insight into the true language of mathematics.

A Transition to Advanced Mathematics

Author: Douglas Smith
Publisher: Cengage Learning
ISBN: 1285463269
Format: PDF, ePub, Mobi
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A TRANSITION TO ADVANCED MATHEMATICS helps students to bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.