A Student's Guide to Infinite Series and Sequences
Author: Bach, Jr. (Bernhard W.)
Publisher:
Published: 2018
Total Pages: 202
ISBN-13: 9781107446588
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A Student's Guide to Infinite Series and Sequences
Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
Published: 2018-05-17
Total Pages: 201
ISBN-13: 1108645739
DOWNLOAD EBOOKWhy study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
Theory of Infinite Sequences and Series
Author: Ludmila Bourchtein
Publisher: Springer Nature
Published: 2021-11-13
Total Pages: 388
ISBN-13: 3030794318
DOWNLOAD EBOOKThis textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Infinite Sequences and Series
Author: Konrad Knopp
Publisher: Courier Corporation
Published: 2012-09-14
Total Pages: 212
ISBN-13: 0486152049
DOWNLOAD EBOOKCareful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Theory and Application of Infinite Series
Author: Konrad Knopp
Publisher:
Published: 1928
Total Pages: 596
ISBN-13:
DOWNLOAD EBOOKTrans from the 2nd German ed , pub 1923.
Infinite Series
Author: Isidore Isaac Hirschman
Publisher: Courier Corporation
Published: 2014-08-18
Total Pages: 193
ISBN-13: 0486798240
DOWNLOAD EBOOKText for advanced undergraduate and graduate students examines Taylor series, Fourier series, uniform convergence, power series, and real analytic functions. Appendix covers set and sequence operations and continuous functions. 1962 edition.
A Student's Guide to Fourier Transforms
Author: J. F. James
Publisher: Cambridge University Press
Published: 2011-03-31
Total Pages: 161
ISBN-13: 1139493949
DOWNLOAD EBOOKFourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem, Babinet's principle and dipole arrays.
A Student's Guide to Numerical Methods
Author: Ian H. Hutchinson
Publisher: Cambridge University Press
Published: 2015-04-30
Total Pages: 223
ISBN-13: 1107095670
DOWNLOAD EBOOKThe plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.
Introduction to Real Analysis
Author: William F. Trench
Publisher: Prentice Hall
Published: 2003
Total Pages: 0
ISBN-13: 9780130457868
DOWNLOAD EBOOKUsing an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
Methods of Solving Sequence and Series Problems
Author: Ellina Grigorieva
Publisher: Birkhäuser
Published: 2016-12-09
Total Pages: 294
ISBN-13: 3319456865
DOWNLOAD EBOOKThis book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.
