Search Results: mathematics-for-natural-scientists-fundamentals-and-basics-undergraduate-lecture-notes-in-physics

Mathematics for Natural Scientists

Fundamentals and Basics

Author: Lev Kantorovich

Publisher: Springer

ISBN: 149392785X

Category: Science

Page: 526

View: 6194

This book covers a course of mathematics designed primarily for physics and engineering students. It includes all the essential material on mathematical methods, presented in a form accessible to physics students, avoiding precise mathematical jargon and proofs which are comprehensible only to mathematicians. Instead, all proofs are given in a form that is clear and convincing enough for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each section of the book. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

Mathematics for Natural Scientists II

Advanced Methods

Author: Lev Kantorovich

Publisher: Springer

ISBN: 3319278614

Category: Science

Page: 675

View: 3658

This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.

Basic Concepts in Physics

From the Cosmos to Quarks

Author: Masud Chaichian,Hugo Perez Rojas,Anca Tureanu

Publisher: Springer Science & Business Media

ISBN: 3642195989

Category: Science

Page: 377

View: 5043

"Basic Concepts in Physics: From the Cosmos to Quarks" is the outcome of the authors' long and varied teaching experience in different countries and for different audiences, and gives an accessible and eminently readable introduction to all the main ideas of modern physics. The book’s fresh approach, using a novel combination of historical and conceptual viewpoints, makes it ideal complementary reading to more standard textbooks. The first five chapters are devoted to classical physics, from planetary motion to special relativity, always keeping in mind its relevance to questions of contemporary interest. The next six chapters deal mainly with newer developments in physics, from quantum theory and general relativity to grand unified theories, and the book concludes by discussing the role of physics in living systems. A basic grounding in mathematics is required of the reader, but technicalities are avoided as far as possible; thus complex calculations are omitted so long as the essential ideas remain clear. The book is addressed to undergraduate and graduate students in physics and will also be appreciated by many professional physicists. It will likewise be of interest to students, researchers and teachers of other natural sciences, as well as to engineers, high-school teachers and the curious general reader, who will come to understand what physics is about and how it describes the different phenomena of Nature. Not only will readers of this book learn much about physics, they will also learn to love it.

Mathematical Physics

A Modern Introduction to Its Foundations

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 3319011952

Category: Science

Page: 1205

View: 2408

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics.

Physics I For Dummies

Author: Steven Holzner

Publisher: John Wiley & Sons

ISBN: 111806755X

Category: Science

Page: 408

View: 7124

Physics I For Dummies, 2nd Edition (9780470903247) is now being published as Physics I For Dummies, 2nd Edition (9781119293590). While this version features an older Dummies cover and design, the content is the same as the new release and should not be considered a different product. The fun and easy way to get up to speed on the basic concepts of physics For high school and undergraduate students alike, physics classes are recommended or required courses for a wide variety of majors, and continue to be a challenging and often confusing course. Physics I For Dummies tracks specifically to an introductory course and, keeping with the traditionally easy-to-follow Dummies style, teaches you the basic principles and formulas in a clear and concise manner, proving that you don't have to be Einstein to understand physics! Explains the basic principles in a simple, clear, and entertaining fashion New edition includes updated examples and explanations, as well as the newest discoveries in the field Contains the newest teaching techniques If just thinking about the laws of physics makes your head spin, this hands-on, friendly guide gets you out of the black hole and sheds light on this often-intimidating subject.

Quantum Mechanics for Pedestrians 1: Fundamentals

Author: Jochen Pade

Publisher: Springer Science & Business Media

ISBN: 331900798X

Category: Science

Page: 452

View: 2337

This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix collects compactly the most important mathematical tools that supplementary literature can be largely dispensed. In addition, the appendix contains advanced topics, such as Quantum- Zeno effect, time-delay experiments, Lenz vector and the Shor algorithm. About 250 exercises, most of them with solutions, help to deepen the understanding of the topics.

Physics from Symmetry

Author: Jakob Schwichtenberg

Publisher: Springer

ISBN: 3319666312

Category: Science

Page: 287

View: 5730

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Mathematical Methods for Physics and Engineering

A Comprehensive Guide

Author: K. F. Riley,M. P. Hobson,S. J. Bence

Publisher: Cambridge University Press

ISBN: 1139450999

Category: Science

Page: N.A

View: 8404

The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

Quantum Theory of the Solid State

An Introduction

Author: Lev Kantorovich

Publisher: Springer Science & Business Media

ISBN: 9781402018213

Category: Science

Page: 626

View: 6435

"Quantum Physics of the Solid State: an Introduction" Draft foreword: 26/09/03 If only this book had been available when I was starting out in science! It would have saved me countless hours of struggle in trying to apply the general ideas of the standard solid-state text-books to solve real problems. The fact is that most of the texts stop at the point where the real difficulties begin. The great merit of this book is that it describes in an honest and detailed way what one really has to do in order to understand the multifarious properties of solids in terms of the fundamental physical theory of quantum mechanics. University students of the physical sciences are taught about the fundamental the ories, and know that quantum mechanics, together with relativity, is our basis for understanding the physical world. But the practical difficulties of using quantum mechanics to do anything useful are usually not very well explained. The truth is that the application of quantum theory to achieve our present detailed understand ing of solids has required the development of a large array of mathematical tech niques. This is closely analogous to the challenge faced long ago by theoretical astronomers in trying to apply Newton's equations of motion to the heavens -they too had to develop a battery of theoretical and computational techniques to do cal culations that could be compared with observation.

Bayesian Probability Theory

Applications in the Physical Sciences

Author: Wolfgang von der Linden,Volker Dose,Udo von Toussaint

Publisher: Cambridge University Press

ISBN: 1107035902

Category: Mathematics

Page: 649

View: 6186

Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.

Introduction to the Foundations of Applied Mathematics

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 0387877657

Category: Mathematics

Page: 468

View: 6523

FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.

Lectures on Groups and Vector Spaces for Physicists

Author: C J Isham

Publisher: World Scientific

ISBN: 9814507296

Category: Science

Page: 228

View: 3638

These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of “Algebra and Groups” is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine “mathematical” thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters. Contents:GroupsVector SpacesGroup Representations Readership: Mathematical physicists and mathematicians.

Higher Mathematics for Physics and Engineering

Author: Hiroyuki Shima,Tsuneyoshi Nakayama

Publisher: Springer Science & Business Media

ISBN: 9783540878643

Category: Science

Page: 688

View: 5967

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are: - Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis. This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

Stochastic Tools in Mathematics and Science

Author: Alexandre J Chorin,Ole H Hald

Publisher: Springer Science & Business Media

ISBN: 1441910026

Category: Mathematics

Page: 162

View: 3483

This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.

Mathematical Methods in Physics

Distributions, Hilbert Space Operators, and Variational Methods

Author: Philippe Blanchard,Erwin Bruening

Publisher: Springer Science & Business Media

ISBN: 1461200490

Category: Mathematics

Page: 471

View: 7605

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Mathematics for Physicists and Engineers

Fundamentals and Interactive Study Guide

Author: Klaus Weltner,Sebastian John,Wolfgang J. Weber,Peter Schuster,Jean Grosjean

Publisher: Springer

ISBN: 3642541240

Category: Science

Page: 602

View: 5452

This textbook offers an accessible approach to the subject of mathematics which divides the topic into smaller units, guiding students through questions, exercises and problems designed to slowly increase student confidence and experience. The sequence of studies is individualised according to performance and can be regarded as full tutorial course. The study guide satisfies two objectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offers advice on the improvement of study skills. Empirical studies have shown that the student's competence for using written information has improved significantly by using this study guide. The new edition includes a new chapter on Fourier integrals and Fourier transforms, numerous sections had been updated, 30 new problems with solutions had been added. The interactive study guide has seen a substantial update.

MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES, 3RD ED

Author: Boas

Publisher: John Wiley & Sons

ISBN: 9788126508105

Category: Mathematics

Page: 864

View: 8276

Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.

The Physics of Information Technology

Author: Neil Gershenfeld

Publisher: Cambridge University Press

ISBN: 9780521580441

Category: Computers

Page: 370

View: 9784

A companion volume to the best-selling The Nature of Mathematical Modeling from the same author, first published in 2000.

A Primer on Scientific Programming with Python

Author: Hans Petter Langtangen

Publisher: Springer

ISBN: 3662498871

Category: Computers

Page: 922

View: 1474

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015

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