Physics For Scientists And Engineers 4th Pdf

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Book Preface

I was motivated from the beginning to write a textbook different from others that
present physics as a sequence of facts, like a Sears catalog: “here are the facts and
you better learn them.” Instead of that approach in which topics are begun
formally and dogmatically, I have sought to begin each topic with concrete
observations and experiences students can relate to: start with specifics and only then
go to the great generalizations and the more formal aspects of a topic, showing why
we believe what we believe. This approach reflects how science is actually practiced.

Why a Fourth Edition?

Download Full PDF Package. A short summary of this paper. 12 Full PDFs related to this paper. Physics for Scientists and Engineers 8th Edition. PDF Drive - Search and download PDF files for free. Giancoli Physics 4th Edition. Download Giancoli Physics 4th Edition. Giancoli Physics for Scientists and Engineers 4th Edition PDF Free Download, Read online, ISBN: By Douglas C. Giancoli Download with Format. Physics for Scientists & Engineers with Modern Physics, Vol.

Unlike static PDF Physics For Scientists & Engineers, Vol. 1 (Chs 1-20) 4th Edition solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn.

Two recent trends in physics texbooks are disturbing: (1) their revision cycles

have become short—they are being revised every 3 or 4 years; (2) the books are
getting larger, some over 1500 pages. I don’t see how either trend can be of
benefit to students. My response: (1) It has been 8 years since the previous
edition of this book. (2) This book makes use of physics education research,
although it avoids the detail a Professor may need to say in class but in a book shuts
down the reader. And this book still remains among the shortest.

This new edition introduces some important new pedagogic tools. It contains
new physics (such as in cosmology) and many new appealing applications (list on
previous page). Pages and page breaks have been carefully formatted to make the
physics easier to follow: no turning a page in the middle of a derivation or Example.
Great efforts were made to make the book attractive so students will want to read it.
Some of the new features are listed below.

What’s New

Chapter-Opening Questions: Each Chapter begins with a multiple-choice question,
whose responses include common misconceptions. Students are asked to answer
before starting the Chapter, to get them involved in the material and to get any
preconceived notions out on the table. The issues reappear later in the Chapter,
usually as Exercises, after the material has been covered. The Chapter-Opening
Questions also show students the power and usefulness of Physics.

APPROACH paragraph in worked-out numerical Examples . A short introductory
paragraph before the Solution, outlining an approach and the steps we can take to
get started. Brief NOTES after the Solution may remark on the Solution, may give
an alternate approach, or mention an application.

Step-by-Step Examples: After many Problem Solving Strategies (more than 20 in
the book), the next Example is done step-by-step following precisely the steps just
seen.

Exercises within the text, after an Example or derivation, give students a chance to
see if they have understood enough to answer a simple question or do a simple
calculation. Many are multiple choice.

Greater clarity : No topic, no paragraph in this book was overlooked in the search
to improve the clarity and conciseness of the presentation. Phrases and sentences
that may slow down the principal argument have been eliminated: keep to the
essentials at first, give the elaborations later.

F, y, B Vector notation, arrows: The symbols for vector quantities in the text and Figures
now have a tiny arrow over them, so they are similar to what we write by hand.
Cosmological Revolution: With generous help from top experts in the field,
readers have the latest results.

Page layout: more than in the previous edition, serious attention has been paid to
how each page is formatted. Examples and all important derivations and
arguments are on facing pages. Students then don’t have to turn back and forth.
Throughout, readers see, on two facing pages, an important slice of physics.
New Applications’. LCDs, digital cameras and electronic sensors (CCD, CMOS),
electric hazards, GFCIs, photocopiers, inkjet and laser printers, metal detectors,
underwater vision, curve balls, airplane wings, DNA, how we actually see images.
(Turn back a page to see a longer list.)

Physics For Scientists And Engineers 4th Pdf

Examples modified: more math steps are spelled out, and many new Examples
added. About 10% of all Examples are Estimation Examples.

This Book is Shorter than other complete full-service books at this level. Shorter
explanations are easier to understand and more likely to be read.
Content and Organizational Changes
• Rotational Motion: Chapters 10 and 11 have been reorganized. All of angular
momentum is now in Chapter 11.
• First law of thermodynamics, in Chapter 19, has been rewritten and extended.
The full form is given: AK + A U + A Eint = Q — W, where internal energy is
Ete, and U is potential energy; the form Q — W is kept so that dW = P dV.
• Kinematics and Dynamics of Circular Motion are now treated together in
Chapter 5.
• Work and Energy, Chapters 7 and 8, have been carefully revised.
• Work done by friction is discussed now with energy conservation (energy
terms due to friction).
• Chapters on Inductance and AC Circuits have been combined into one:
Chapter 30.
• Graphical Analysis and Numerical Integration is a new optional Section 2-9.
Problems requiring a computer or graphing calculator are found at the end
of most Chapters.
• Length of an object is a script £ rather than normal /, which looks like 1 or I
(moment of inertia, current), as in F = IIB. Capital L is for angular
momentum, latent heat, inductance, dimensions of length [L.
• Newton’s law of gravitation remains in Chapter 6. Why? Because the 1/r2
law is too important to relegate to a late chapter that might not be covered
at all late in the semester; furthermore, it is one of the basic forces in nature.
In Chapter 8 we can treat real gravitational potential energy and have a fine
instance of using U = – JF • di.
• New Appendices include the differential form of Maxwell’s equations and
more on dimensional analysis.
• Problem Solving Strategies are found on pages 30, 58, 64, 96,102,125,166,
198,229,261,314,504,551,571, 685,716,740,763,849, 871, and 913.
Organization
Some instructors may find that this book contains more material than can be
covered in their courses. The text offers great flexibility. Sections marked with a
star * are considered optional. These contain slightly more advanced physics
material, or material not usually covered in typical courses and/or interesting
applications; they contain no material needed in later Chapters (except perhaps in
later optional Sections). For a brief course, all optional material could be dropped
as well as major parts of Chapters 1, 13, 16, 26, 30, and 35, and selected parts of
Chapters 9,12,19,20, 33, and the modern physics Chapters. Topics not covered in
class can be a valuable resource for later study by students. Indeed, this text can
serve as a useful reference for years because of its wide range of coverage.

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Physics for Scientists and Engineers Volume 2 Chapters 23 46

Author: Raymond A. Serway,John W. Jewett
Publsiher: Cengage Learning
Total Pages: 880
Release: 2010-01-13
ISBN 10: 1439048398
ISBN 13: 9781439048399
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers Volume 2 Chapters 23 46 Book Review:

As a market leader, PHYSICS FOR SCIENTISTS AND ENGINEERS is one of the most powerful brands in the physics market. However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers

Author: Lawrence S. Lerner
Publsiher: Jones & Bartlett Learning
Total Pages: 1137
Release: 1997
ISBN 10: 9780763704605
ISBN 13: 0763704601
Language: EN, FR, DE, ES & NL

This refreshing new text is a friendly companion to help students master the challenging concepts in a standard two-or three-semester, calculus-based physics course. Dr. Lerner carefully develops every concept with detailed explanations while incorporating the mathematical underpinnings of the concepts. This juxtaposition enables students to attain a deeper understanding of physical concepts while developing their skill at manipulating equations.

Physics for Scientists Engineers

Author: Douglas C. Giancoli
Publsiher: Pearson College Division
Total Pages: 1024
Release: 2000
ISBN 10:
ISBN 13: UCSD:31822027911601
Language: EN, FR, DE, ES & NL

Physics for Scientists and Engineers combines outstanding pedagogy with a clear and direct narrative and applications that draw the reader into the physics. The new edition features an unrivaled suite of media and on-line resources that enhance the understanding of physics. Many new topics have been incorporated such as: the Otto cycle, lens combinations, three-phase alternating current, and many more. New developments and discoveries in physics have been added including the Hubble space telescope, age and inflation of the universe, and distant planets. Modern physics topics are often discussed within the framework of classical physics where appropriate. For scientists and engineers who are interested in learning physics.

Physics for Scientists and Engineers with Modern Physics Technology Update

Author: Raymond A. Serway,John W. Jewett
Publsiher: Nelson Education
Total Pages: 1616
Release: 2015
ISBN 10: 1305804481
ISBN 13: 9781305804487
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers with Modern Physics Technology Update Book Review:

Achieve success in your physics course by making the most of what PHYSICS FOR SCIENTISTS AND ENGINEERS has to offer. From a host of in-text features to a range of outstanding technology resources, you’ll have everything you need to understand the natural forces and principles of physics. Throughout every chapter, the authors have built in a wide range of examples, exercises, and illustrations that will help you understand the laws of physics AND succeed in your course! Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers Volume 5 Chapters 40 46

Author: Raymond Serway,John Jewett
Publsiher: Nelson Education
Total Pages: 368
Release: 2010-01-12
ISBN 10: 111178891X
ISBN 13: 9781111788919
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers Volume 5 Chapters 40 46 Book Review:

As a market leader, PHYSICS FOR SCIENTISTS AND ENGINEERS is one of the most powerful brands in the physics market. However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists Engineers with Modern Physics

Author: Douglas C. Giancoli
Publsiher: Pearson Education
Total Pages: 1228
Release: 2008
ISBN 10: 0131495089
ISBN 13: 9780131495081
Language: EN, FR, DE, ES & NL
Physics for Scientists Engineers with Modern Physics Book Review:

Key Message: This book aims to explain physics in a readable and interesting manner that is accessible and clear, and to teach readers by anticipating their needs and difficulties without oversimplifying. Physics is a description of reality, and thus each topic begins with concrete observations and experiences that readers can directly relate to. We then move on to the generalizations and more formal treatment of the topic. Not only does this make the material more interesting and easier to understand, but it is closer to the way physics is actually practiced. Key Topics: INTRODUCTION, MEASUREMENT, ESTIMATING, DESCRIBING MOTION: KINEMATICS IN ONE DIMENSION, KINEMATICS IN TWO OR THREE DIMENSIONS; VECTORS, DYNAMICS: NEWTON'S LAWS OF MOTION , USING NEWTON'S LAWS: FRICTION, CIRCULAR MOTION, DRAG FORCES, GRAVITATION AND NEWTON'S6 SYNTHESIS , WORK AND ENERGY , CONSERVATION OF ENERGY , LINEAR MOMENTUM , ROTATIONAL MOTION , ANGULAR MOMENTUM; GENERAL ROTATION , STATIC EQUILIBRIUM; ELASTICITY AND FRACTURE , FLUIDS , OSCILLATIONS , WAVE MOTION, SOUND , TEMPERATURE, THERMAL EXPANSION, AND THE IDEAL GAS LAW KINETIC THEORY OF GASES, HEAT AND THE FIRST LAW OF THERMODYNAMICS , SECOND LAW OF THERMODYNAMICS , ELECTRIC CHARGE AND ELECTRIC FIELD , GAUSS'S LAW , ELECTRIC POTENTIAL , CAPACITANCE, DIELECTRICS, ELECTRIC ENERGY STORAGE ELECTRIC CURRENTS AND RESISTANCE, DC CIRCUITS, MAGNETISM, SOURCES OF MAGNETIC FIELD, ELECTROMAGNETIC INDUCTION AND FARADAY'S LAW, INDUCTANCE, ELECTROMAGNETIC OSCILLATIONS, AND AC CIRCUITS, MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES, LIGHT: REFLECTION AND REFRACTION, LENSES AND OPTICAL INSTRUMENTS, THE WAVE NATURE OF LIGHT; INTERFERENCE, DIFFRACTION AND POLARIZATION, SPECIAL THEORY OF RELATIVITY, EARLY QUANTUM THEORY AND MODELS OF THE ATOM, QUANTUM MECHANICS, QUANTUM MECHANICS OF ATOMS, MOLECULES AND SOLIDS, NUCLEAR PHYSICS AND RADIOACTIVITY, NUCLEAR ENERGY: EFECTS AND USES OF RADIATION, ELEMENTARY PARTICLES,ASTROPHYSICS AND COSMOLOGY Market Description: This book is written for readers interested in learning the basics of physics.

Physics for Scientists and Engineers

Author: Raymond A. Serway,John W. Jewett
Publsiher: Cengage Learning
Total Pages: 1296
Release: 2018-01-01
ISBN 10: 1337553271
ISBN 13: 9781337553278
Language: EN, FR, DE, ES & NL

Achieve success in your physics course by making the most of what Serway/Jewett's PHYSICS FOR SCIENTISTS AND ENGINEERS has to offer. From a host of in-text features to a range of outstanding technology resources, you'll have everything you need to understand the natural forces and principles of physics. Throughout every chapter, the authors have built in a wide range of examples, exercises, and illustrations that will help you understand the laws of physics AND succeed in your course! Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers with Modern Physics

Author: Raymond A. Serway,John W. Jewett
Publsiher: Brooks/Cole Publishing Company
Total Pages: 1552
Release: 2004
ISBN 10: 9780534408541
ISBN 13: 0534408540
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers with Modern Physics Book Review:

The Companion Web Site (http://www.pse6.com), newly revised for this edition, features student access to Quizzes, Web Links, Internet Exercises, Learning Objectives, and Chapter Outlines. Best free apps for mac pro retina upgrade. In addition, instructors have password-protected access to a downloadable file of the Instructor's Manual, a Mulitmedia Manager demo, and PowerPointʼ files of QUICK QUIZZES.

Physics for Scientists and Engineers Volume 1 Chapters 1 22

Author: Raymond A. Serway,John W. Jewett
Publsiher: Cengage Learning
Total Pages: 736
Release: 2009-07-30
ISBN 10: 143904838X
ISBN 13: 9781439048382
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers Volume 1 Chapters 1 22 Book Review:

As a market leader, PHYSICS FOR SCIENTISTS AND ENGINEERS is one of the most powerful brands in the physics market. However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers Chapters 1 39

Author: Raymond A. Serway,John W. Jewett
Publsiher: Cengage Learning
Total Pages: 1296
Release: 2012-02-01
ISBN 10: 0495827819
ISBN 13: 9780495827818
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers Chapters 1 39 Book Review:

As a market leader, PHYSICS FOR SCIENTISTS AND ENGINEERS is one of the most powerful brands in the physics market. However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. While preserving concise language, state of the art educational pedagogy, and top-notch worked examples, the Eighth Edition features a unified art design as well as streamlined and carefully reorganized problem sets that enhance the thoughtful instruction for which Raymond A. Serway and John W. Jewett, Jr. earned their reputations. Likewise, PHYSICS FOR SCIENTISTS AND ENGINEERS will continue to accompany Enhanced WebAssign in the most integrated text-technology offering available today. In an environment where new Physics texts have appeared with challenging and novel means to teach students, this book exceeds all modern standards of education from the most solid foundation in the Physics market today. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers with Modern Physics

And
Author: Raymond A. Serway,Robert J. Beichner
Publsiher: Houghton Mifflin
Total Pages: 1551
Release: 2000
ISBN 10:
ISBN 13: UCSC:32106012356371
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers with Modern Physics Book Review:

This best-selling calculus-based text is recognized for its carefully crafted, logical presentation of the basic concepts and principles of physics. The book is available in single hardcover volumes, 2-volume hardcover sets, and 4- or 5-volume softcover sets. Raymond Serway Robert Beichner, and contributing author John W. Jewett present a strong problem-solving approach that is further enhanced through increased realism in worked examples. Problem-solving strategies and hints allow students to develop a systematic approach to completing homework problems. The outstanding ancillary package includes full multimedia support, online homework, and a content-rich Web site that provides extensive support for instructors and students. The CAPA (Computer-assisted Personalized Approach), WebAssign, and University of Texas homework delivery systems give instructors flexibility in assigning online homework.

Physics for Scientists and Engineers

Physics for scientists and engineers 4th pdf solutionsPhysics for scientists and engineers 5th pdf
Author: Paul A. Tipler,Gene Mosca
Publsiher: Macmillan
Total Pages: 1172
Release: 2007-05-01
ISBN 10: 142920124X
ISBN 13: 9781429201247
Language: EN, FR, DE, ES & NL

The Sixth Edition of Physics for Scientists and Engineers offers a completely integrated text and media solution that will help students learn most effectively and will enable professors to customize their classrooms so that they teach most efficiently. The text includes a new strategic problem-solving approach, an integrated Math Tutorial, and new tools to improve conceptual understanding. To simplify the review and use of the text, Physics for Scientists and Engineers is available in these versions: Volume 1 Mechanics/Oscillations and Waves/Thermodynamics (Chapters 1-20, R) 1-4292-0132-0 Volume 2 Electricity and Magnetism/Light (Chapters 21-33) 1-4292-0133-9 Volume 3 Elementary Modern Physics (Chapters 34-41) 1-4292-0134-7 Standard Version (Chapters 1-33, R) 1-4292-0124-X Extended Version (Chapters 1-41, R) 0-7167-8964-7

Physics for Scientists and Engineers

Author: Raymond A Serway,John W. Jewett,Vahé Peroomian
Publsiher: Thomson Brooks/Cole
Total Pages: 882
Release: 2012-12-18
ISBN 10: 9781285070315
ISBN 13: 1285070313
Language: EN, FR, DE, ES & NL

As a market leader, PHYSICS FOR SCIENTISTS AND ENGINEERS VOLUME 2, 9E, International Edition is one of the most powerful brands in the physics market. While preserving concise language, state-of-the-art educational pedagogy, and top-notch worked examples, the Ninth Edition highlights the Analysis Model approach to problem-solving, including brand-new Analysis Model Tutorials, written by text co-author John Jewett, and available in Enhanced WebAssign. The Analysis Model approach lays out a standard set of situations that appear in most physics problems, and serves as a bridge to help students identify the correct fundamental principle--and then the equation--to utilize in solving that problem. The unified art program and the carefully thought out problem sets also enhance the thoughtful instruction for which Raymond A. Serway and John W. Jewett, Jr. earned their reputations. PHYSICS FOR SCIENTISTS AND ENGINEERS VOLUME 2, 9E, International Edition continues to be accompanied by Enhanced WebAssign in the most integrated text-technology offering available today.

Physics for Scientists and Engineers

Author: Randall Dewey Knight,Randall D. Knight
Publsiher: Addison-Wesley
Total Pages: 1308
Release: 2013
ISBN 10: 9780321753151
ISBN 13: 0321753151
Language: EN, FR, DE, ES & NL

Description based on: v. 4, copyrighted in 2013.

Physics for Scientists and Engineers Chapters 1 39

Author: Raymond Serway,John Jewett
Publsiher: Cengage Learning
Total Pages: 1248
Release: 2007-02-20
ISBN 10: 0495013129
ISBN 13: 9780495013129
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers Chapters 1 39 Book Review:

PHYSICS FOR SCIENTISTS AND ENGINEERS reveals the beauty and simplicity of physics while highlighting its essential role in other disciplines, from engineering to medicine. This proven text features the Serway hallmarks of concise writing, carefully thought-out problem sets, world class worked examples, and leading-edge educational pedagogy. With the Seventh Edition, authors Raymond A. Serway and John W. Jewett, Jr. build upon this strong foundation by carrying that high standard to the book's carefully integrated technology package, perfectly tailored to support any course design. All end-of-chapter problems, worked examples, and quick quizzes are available in Enhanced WebAssign (with hints and feedback formulated to foster student learning), allowing instructors to securely create and administer homework assignments in an interactive online environment. For instructors utilizing classroom response technology, a complete suite of PowerPoint-formatted questions designed to support all levels of users, from amateur through advanced, is available to support the clicker software of your choosing. The result is the most complete course solution you will find; and one that is scalable to meet your and your students' unique needs. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists Engineers

Author: Raymond A. Serway
Publsiher: Harcourt Brace College Publishers
Total Pages: 720
Release: 1996
ISBN 10:
ISBN 13: UCSD:31822027843937
Language: EN, FR, DE, ES & NL

This revised calculus-based physics text has a problem solving approach, incorporating intermediate and challenging problems, spreadsheet problems, and conceptual problems with reasoning statements.

Physics for Scientists and Engineers with Modern Physics

Author: John W. Jewett,Raymond A. Serway
Publsiher: Cengage Learning EMEA
Total Pages: 1392
Release: 2008
ISBN 10: 9780495112402
ISBN 13: 0495112402
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers with Modern Physics Book Review:

Achieve success in your physics course by making the most of what PHYSICS FOR SCIENTISTS AND ENGINEERS has to offer you. From a host of in-text features to a range of outstanding technology resources, you'll have everything you need to understand the natural forces and principles of physics. Throughout every chapter, the authors have built in a wide range of examples, exercises, and illustrations that will help you understand the laws of physics AND succeed in your course!Available with most new copies of the text is CengageNOW for Physics. Save time, learn more, and succeed in the course with this online suite of resources that give you the choices and tools you need to study smarter and get the grade. Receive a personalized study plan based on chapter-specific diagnostic testing to help you pinpoint what you need to know NOW, and interact with a live physics tutor through the exclusive vMentor program to help you master the concepts.

Physics for scientists and engineers

Author: Paul A. Tipler
Publsiher: Anonim
Total Pages: 329
Release: 2008
ISBN 10: 9781319155988
ISBN 13: 1319155987
Language: EN, FR, DE, ES & NL

Physics for Scientists and Engineers with Modern Physics Chapters 39 46

And
Author: Raymond Serway,John Jewett
Publsiher: Cengage Learning
Total Pages: 1184
Release: 2007-06-12
ISBN 10: 9780495112938
ISBN 13: 0495112933
Language: EN, FR, DE, ES & NL
Physics for Scientists and Engineers with Modern Physics Chapters 39 46 Book Review:

PHYSICS FOR SCIENTISTS AND ENGINEERS reveals the beauty and simplicity of physics while highlighting its essential role in other disciplines, from engineering to medicine. This proven text features the Serway hallmarks of concise writing, carefully thought-out problem sets, world class worked examples, and leading-edge educational pedagogy. With the Seventh Edition, authors Raymond A. Serway and John W. Jewett, Jr. build upon this strong foundation by carrying that high standard to the book's carefully integrated technology package, perfectly tailored to support any course design. All end-of-chapter problems, worked examples, and quick quizzes are available in Enhanced WebAssign (with hints and feedback formulated to foster student learning), allowing instructors to securely create and administer homework assignments in an interactive online environment. For instructors utilizing classroom response technology, a complete suite of PowerPoint-formatted questions designed to support all levels of users, from amateur through advanced, is available to support the clicker software of your choosing. The result is the most complete course solution you will find; and one that is scalable to meet your and your students' unique needs. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Physics for Scientists and Engineers

Author: Lawrence S. Lerner
Publsiher: Jones & Bartlett Learning
Total Pages: 1137
Release: 1996
ISBN 10: 9780867204797
ISBN 13: 0867204796
Language: EN, FR, DE, ES & NL

Physics For Scientists And Engineers 4th Pdf

This refreshing new text is a friendly companion to help students master the challenging concepts in a standard two- or three-semester, calculus-based physics course. Dr. Lerner carefully develops every concept with detailed explanations while incorporating the mathematical underpinnings of the concepts. This juxtaposition enables students to attain a deeper understanding of physical concepts while developing their skill at manipulating equations.