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Problem-solving is the cornerstone of all walks of scientific research. Fascinating Problems for Young Physicists attempts to clear the boundaries of seemingly abstract physical laws and their tangible effects through a step-by-step approach to physics in the world around us. It consists of 42 problems with detailed solutions, each describing a specific, interesting physical phenomenon. Each problem is further divided into questions designed to guide the reader through, encouraging engagement with and learning the physics behind the phenomenon. By solving the problems, the reader will be able to discover, for example, what the relation is between the mass of an animal and its expected lifetime, or what the efficiency limit is of wind turbines. Intended for first-year undergraduate students and interested high school students, this book develops inquiry-based scientific practice and enables students to acquire the necessary skills for applying the laws of physics to realistic situations.
This advanced undergraduate physics textbook presents an accessible treatment of classical mechanics using plain language and clear examples. While comprehensive, the book can be tailored to a one-semester course. An early introduction of the Lagrangian and Hamiltonian formalisms gives students an opportunity to utilize these important techniques in the easily visualized context of classical mechanics. The inclusion of 321 simple in-chapter exercises, 82 worked examples, 550 more challenging end-of-chapter problems, and 65 computational projects reinforce students' understanding of key physical concepts and give instructors freedom to choose from a wide variety of assessment and support materials. This new edition has been reorganized. Numerous sections were rewritten. New problems, a chapter on fluid dynamics, and brief optional studies of advanced topics such as general relativity and orbital mechanics have been incorporated. Online resources include a solutions manual for instructors, lecture slides, and a set of student-oriented video lectures.
This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates – length contraction and time dilation – are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.
The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.
Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.
In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with his gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists.
This is the first comprehensive overview of the 'science of science,' an emerging interdisciplinary field that relies on big data to unveil the reproducible patterns that govern individual scientific careers and the workings of science. It explores the roots of scientific impact, the role of productivity and creativity, when and what kind of collaborations are effective, the impact of failure and success in a scientific career, and what metrics can tell us about the fundamental workings of science. The book relies on data to draw actionable insights, which can be applied by individuals to further their career or decision makers to enhance the role of science in society. With anecdotes and detailed, easy-to-follow explanations of the research, this book is accessible to all scientists and graduate students, policymakers, and administrators with an interest in the wider scientific enterprise.
In this modern and distinctive textbook, Helliwell and Sahakian present classical mechanics as a thriving and contemporary field with strong connections to cutting-edge research topics in physics. Each part of the book concludes with a capstone chapter describing various key topics in quantum mechanics, general relativity, and other areas of modern physics, clearly demonstrating how they relate to advanced classical mechanics, and enabling students to appreciate the central importance of classical mechanics within contemporary fields of research. Numerous and detailed examples are interleaved with theoretical content, illustrating abstract concepts more concretely. Extensive problem sets at the end of each chapter further reinforce students' understanding of key concepts, and provide opportunities for assessment or self-testing. A detailed online solutions manual and lecture slides accompany the text for instructors. Often a flexible approach is required when teaching advanced classical mechanics, and, to facilitate this, the authors have outlined several paths instructors and students can follow through the book, depending on background knowledge and the length of their course.
Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insights emerging from Franklin's treatment make it a valuable teaching resource.
Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.
Written in easily accessible language, the book provides a modern perspective of classical mechanics. Mathematical rigour is intertwined with lucid narration that will generate confidence in students to assimilate and apply fundamental principles of physics. The commonalities and differences of Newton's, Lagrange's and Hamilton's equations are explained in detail. Free, damped, driven oscillators and resonances are analysed systematically. The text extensively covers concepts of fluid mechanics, special theory of relativity, general theory of relativity and Lorentz transformations. The theories of gravitational field, fractals and chaos, Maxwell's laws of electrodynamics, and Einstein's theory of relativity are expanded from the first principle. The text is supported by practice problem sets to help students check their understanding of the concepts.
Responding to the developments of the past twenty years, Les Kirkup has thoroughly updated his popular book on experimental methods, while retaining the extensive coverage and practical advice from the first edition. Many topics from that edition remain, including keeping a record of work, how to deal with measurement uncertainties, understanding the statistical basis of data analysis and reporting the results of experiments. However, with new technologies influencing how experiments are devised, carried out, analyzed, presented and reported, this new edition reflects the digital changes which have taken place and the increased emphasis on the importance of communication skills in reporting results. Bringing together key elements of experimental methods into one coherent book, it is perfect for students seeking guidance with their experimental work, including how to acquire, analyse and present data. Exercises, worked examples and end-of-chapter problems are provided throughout the book to reinforce fundamental principles.
Classical field theory predicts how physical fields interact with matter, and is a logical precursor to quantum field theory. This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern–Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.
An essential part of studying to become a physical scientist or engineer is learning how to solve problems. This book contains over 200 appropriate physics problems with hints and full solutions. The author demonstrates how to break down a problem into its essential components, and how to chart a course through them to a solution. With problem-solving skills being essential for any physical scientist or engineer, this book will be invaluable to potential and current undergraduates seeking a career in these fields. The book is divided into three parts: questions, hints and solutions. The questions section is subdivided into 15 chapters, each centred on a different area of physics, from elementary particles, through classical physics, to cosmology. The second section provides brief hints, whilst the third sets out full and explicit solutions to each problem. Most begin with thoughts that students might have after reading a problem, allowing the reader to understand which questions they should be asking themselves when faced with unfamiliar situations.
This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.
In this introductory textbook, thermodynamics is presented as a natural extension of mechanics, so that the laws and concepts learned in mechanics serve to get acquainted with the theory. The foundations of thermodynamics are presented in the first part. The second part covers a wide range of applications, which are of central importance in the fields of physics, chemistry and engineering, including calorimetry, phase transitions, heat engines and chemical reactions. In the third part, devoted to continuous media, Fourier and Fick's laws, diffusion equations and many transport effects are derived using a unified approach. Each chapter concludes with a selection of worked examples and several exercises, to reinforce key concepts under discussion. A full solutions manual is available at the end of the book. It contains more than 150 problems based on contemporary issues faced by scientists and engineers that are solved in detail for undergraduate and graduate students.
Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics.
This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.
The Physics GRE plays a significant role in deciding admissions to nearly all US physics Ph.D. programs, yet few exam-prep books focus on the test's actual content and unique structure. Recognized as one of the best student resources available, this tailored guide has been thoroughly updated for the current Physics GRE. It contains carefully selected review material matched to all of the topics covered, as well as tips and tricks to help solve problems under time pressure. It features three full-length practice exams, revised to accurately reflect the difficulty of the current test, with fully worked solutions so that students can simulate taking the test, review their preparedness, and identify areas in which further study is needed. Written by working physicists who took the Physics GRE for their own graduate admissions to the Massachusetts Institute of Technology, this self-contained reference guide will help students achieve their best score.
The Physics of Energy provides a comprehensive and systematic introduction to the scientific principles governing energy sources, uses, and systems. This definitive textbook traces the flow of energy from sources such as solar power, nuclear power, wind power, water power, and fossil fuels through its transformation in devices such as heat engines and electrical generators, to its uses including transportation, heating, cooling, and other applications. The flow of energy through the Earth's atmosphere and oceans, and systems issues including storage, electric grids, and efficiency and conservation are presented in a scientific context along with topics such as radiation from nuclear power and climate change from the use of fossil fuels. Students, scientists, engineers, energy industry professionals, and concerned citizens with some mathematical and scientific background who wish to understand energy systems and issues quantitatively will find this textbook of great interest.