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Lectures On Complex Integration

Author: Alexander O. Gogolin
Publisher: Springer Science & Business Media
ISBN: 3319002120
Size: 62.49 MB
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The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

Inside Interesting Integrals

Author: Paul J. Nahin
Publisher: Springer
ISBN: 9781493912766
Size: 51.72 MB
Format: PDF
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What’s the point of calculating definite integrals since you can’t possibly do them all?. What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.

Mathematical Methods

Author: Sadri Hassani
Publisher: Springer Science & Business Media
ISBN: 038721562X
Size: 68.33 MB
Format: PDF
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Intended to follow the usual introductory physics courses, this book contains many original, lucid and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts to help guide students through the material.

Introduction To Methods Of Approximation In Physics And Astronomy

Author: Maurice H. P. M. van Putten
Publisher: Springer
ISBN: 9811029326
Size: 50.35 MB
Format: PDF, ePub
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This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing. Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.

The Physics Of Living Systems

Author: Fabrizio Cleri
Publisher: Springer
ISBN: 3319306472
Size: 22.69 MB
Format: PDF, Kindle
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In this book, physics in its many aspects (thermodynamics, mechanics, electricity, fluid dynamics) is the guiding light on a fascinating journey through biological systems, providing ideas, examples and stimulating reflections for undergraduate physics, chemistry and life-science students, as well as for anyone interested in the frontiers between physics and biology. Rather than introducing a lot of new information, it encourages young students to use their recently acquired knowledge to start seeing the physics behind the biology. As an undergraduate textbook in introductory biophysics, it includes the necessary background and tools, including exercises and appendices, to form a progressive course. In this case, the chapters can be used in the order proposed, possibly split between two semesters. The book is also an absorbing read for researchers in the life sciences who wish to refresh or go deeper into the physics concepts gleaned in their early years of scientific training. Less physics-oriented readers might want to skip the first chapter, as well as all the "gray boxes" containing the more formal developments, and create their own á-la-carte menu of chapters.

An Introduction To Complex Analysis

Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 9781461401957
Size: 76.51 MB
Format: PDF, ePub, Docs
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This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Lectures On Selected Topics In Mathematical Physics

Author: William A. Schwalm
Publisher: Morgan & Claypool Publishers
ISBN: 1681740389
Size: 63.46 MB
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This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Lectures On Measure And Integration

Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810283
Size: 57.25 MB
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These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

Elementary Mechanics Using Python

Author: Anders Malthe-Sorenssen
Publisher: Springer
ISBN: 3319195964
Size: 63.46 MB
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This book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks. Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts. While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Python, and a chapter devoted to the basics of scientific programming with Python is included. A parallel edition using Matlab instead of Python is also available. Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.