Like having a private coach at their elbows, this introduction to algebra-based physics involves readers *actively* in a guided learn-by-doing process—sensing when they need a very patient exposition and when they need only minimal reinforcement, when they need to focus on concepts and when they need an opportunity to practice their quantitative skills. At the heart of the volume are worked examples in a unique, two-column format that focuses on the basic strategies and step-by-step *thought processes* involved in problem solving—with an emphasis on the *relationship* between the physical concepts and their mathematical expression. Color-coded drawings help readers visualize physics problems, and companion photographs show the same principle at work in different physical contexts, or juxtapose situations in which contrasting principles are at work. Real-world physics applications abound. Covers the full spectrum of topics in Mechanics, Thermal Physics, Electromagnetism, Light and Optics, and Modern Physics. For anyone needing an introduction to, or refresher of, algebra-based physics.

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** James S. Walker.** James Walker obtained his Ph.D. in theoretical physics from the University of Washington in 1978. He subsequently served as a post-doc at the University of Pennsylvania, the Massachusetts Institute of Technology, and the University of California at San Diego before joining the physics faculty at Washington State University in 1983. Professor Walker's research interests include statistical mechanics, critical phenomena, and chaos. His many publications on the application of renormalization-group theory to systems ranging from absorbed monolayers to binary-fluid mixtures have appeared in

Jim Walker likes to work with students at all levels, from judging elementary school science fairs to writing research papers with graduate students, and has taught introductory physics for many years. His enjoyment of this course and his empathy for students have earned him a reputation as an innovative, enthusiastic, and effective teacher. Jim's educational publications include "Reappearing Phases" (*Scientific American,* May 1987) as well as articles in the *American Journal of Physics* and *The Physics Teacher.* In recognition of his contributions to the teaching of physics, Jim was named Boeing Distinguished Professor of Science and Mathematics Education for 2001-2003.

When he is not writing, conducting research, teaching, or developing new classroom demonstrations and pedagogical materials, Jim enjoys amateur astronomy, bird watching, photography, juggling, unicycling, boogie boarding, and kayaking. Jim is also an avid jazz pianist and organist. He has served as ballpark organist for several Class A minor league baseball teams, including minor league affiliates of the Seattle Mariners and San Francisco Giants.

**To the Instructor**

Teaching introductory algebra-based physics can be a most challenging and rewarding experience. Students enter the course with a wide range of backgrounds, interests, and skills and we, the instructors, strive not only to convey the basic concepts and fundamental laws of physics, but also to give students an appreciation of its relevance and appeal.

I wrote this book to help with that task. It incorporates a number of unique and innovative pedagogical features that evolved from years of teaching experience. The materials have been tested extensively in the classroom and in focus groups, and refined based on comments from students and teachers who used the first edition. The enthusiastic response I received from users of the first edition was both flattering and motivating. The second edition has been enhanced and enriched in response to this feedback.

**Learning Tools in the Text**

A key goal of this text is to help students make the connection between a conceptual understanding of physics and the various skills necessary to solve quantitative problems. One of the chief means to that end is the replacement of traditional "textbook". Examples with an integrated suite of learning tools: fully worked *Examples with Solutions in Two-Column Format, Active Examples, Conceptual Checkpoints,* and *Exercises.* Each of these tools performs some of the functions of a standard Example, but each is specialized to meet the needs of students at a particular point in the development of a chapter.

These needs are not always the same. Sometimes students require a detailed explanation of how to tackle a particular problem; at other times, they must be allowed to take an active role and work out the details for themselves. Sometimes it is important for them to perform calculations and concentrate on numerical precision; at other times it is more fruitful for them to explore a key idea in a conceptual context. And sometimes, all that is required is practice using a new equation or definition.

A good teacher can sense when students need a patient, step-by-step exposition and when they need only minimal reinforcement; when they need to focus on concepts and when they need an opportunity to practice their quantitative skills. This text attempts to emulate the teaching style of successful instructors by providing the right tool at the right time and place.

**Worked Examples with Solutions in Two-Column Format**

*Examples* model the most complete and detailed method of solving a particular type of problem. The Examples in this text are presented in a format that focuses on the basic strategies and thought processes involved in problem solving. The aim of this approach is to help students first visualize the situation, devise a *strategy* to be followed, and then implement a clear *step-by-step solution* to the problem. This focus on the intimate relationship between conceptual insights and problem-solving techniques encourages students to view the ability to solve problems as a logical outgrowth of conceptual understanding rather than a kind of parlor trick.

Each Example has the same basic structure:

**Picture the Problem.**This first step discusses how the physical situation can be represented visually and what such a representation can tell us about how to analyze and solve the problem. At this step, always accompanied by a figure, we set up a coordinate system where appropriate, label important quantities, and indicate which values are known. The*Picture the Problem*steps have been enhanced in the second edition to make them more instructive.**Strategy.**Closely linked with this visualization process is the formulation of a*Strategy*to be followed in solving the problem. The strategy addresses the commonly asked question, "How do I get started?" by providing a clear overview of the problem and helping students to identify the relevant physical principles. It then guides the student in using known relationships to map a step-by-step path to the solution.**Solution in Two Column Format.**In the step-by-step*Solution*of the problem, each of the steps is presented with a prose statement in the left-hand column and the corresponding mathematical implementation in the right-hand column. Each step clearly translates the idea described in words into the appropriate equations. When reviewing an Example, note that the left-hand column gives the flow of ideas used in the solution; the right-hand column gives the mathematical calculations that were carried out.**Insight.**Each Example wraps up with an*Insight*a comment regarding the solution just obtained. Some Insights deal with possible alternative solution techniques, others with new ideas suggested by the results.**Practice Problem.**Following the Insight is a*Practice Problem,*which gives the student a chance to practice the type of calculation just presented. The Practice Problems, always accompanied by their answers, provide students with a valuable check on their understanding of the material. Finally, each Example ends with a reference to some related end-of-chapter problems to allow students to test their skills further.

**Active Examples**

*Active Examples* serve as a bridge between the fully worked Examples, in which every detail is fully discussed and every step is given, and the homework Problems, where no help is given at all. In an Active Example, students take an active role in solving the problem by thinking through the logic of the steps described on the left and checking their answers on the right. Students often find it useful to practice problem solving by covering one column of an Active Example with a sheet of paper and filling in the covered steps as they refer to the other column. In the second edition, follow-up questions, called Your Turns, ask students to look at the problem in a slightly different way. Answers to Your Turns, are provided at the end of the book. Working through Active Examples will make students better prepared to tackle homework problems on their own.

**Conceptual Checkpoints**

*Conceptual Checkpoints* help students sharpen their insight into key physical principles. A typical Conceptual Checkpoint presents a thought-provoking question that can be answered by logical reasoning based on physical concepts rather than by numerical calculations. These questions, which can be just as challenging as any numerical problem and just as educational, are presented in multiple-choice format to help focus the student's thinking. The statement of the question is followed by a detailed discussion and analysis in the section titled *Reasoning and Discussion,* and the *Answer* is given at the end of the checkpoint for quick and easy reference.

**Exercises**

*Exercises* present brief calculations designed to illustrate the application of important new relationships, without the expenditure of time and space required by a fully worked Example. Exercises generally give students an opportunity to practice the use of a new equation, become familiar with the units of a new physical quantity, and get a feeling for typical magnitudes.

**Problem Solving Notes**

In addition to the in-text elements just described, each chapter includes a number of marginal *Problem Solving Notes.* These practical hints are designed to highlight useful problem-solving methods while helping students avoid common pitfalls Remember to measure angles in radians and misconceptions.

**End of Chapter Learning Tools**

The end of chapter material in this text also includes a number of innovations, along with refinements of more familiar elements.

**Chapter Summary**

Each chapter concludes with a Chapter Summary presented in an easy-to-use outline style. Key concepts and equations are organized by topic for convenient reference.

**Problem-Solving Summary**

A unique feature of this text is the *Problem-Solving Summary* at the end of the chapter. This is a new type of summary that addresses common sources of misconceptions in problem solving, and gives specific references to Examples and Active Examples illustrating the correct procedures. Organized by type of problem, each entry in the Problem-Solving Summary relates a specific type of calculation to the relevant physical concepts.

**Conceptual Questions**

The homework for each chapter begins with a section of *Conceptual Questions.* Answers to the odd-numbered questions can be found in the back of the book, so that students can check their reasoning and conclusions. Answers to even-numbered Conceptual Questions are available in the Instructor's Solutions Manual.

**Numerical and Integrated Homework Problems**

A collection of numerical and Integrated Problems are presented at the end of each chapter. Note that a number of problems are given for each section of the chapter. In addition, a section titled "General Problems" presents a variety of problems that use material from two or more sections within the chapter, or refer to material covered in earlier chapters.

The difficulty of Problems is ranked using one, two, or three blue dots. The most straightforward Problems are labeled with a single dot (·), Problems involving several steps and more detailed reasoning are labeled with two dots (··), and Problems of a more challenging nature are indicated with three dots (···).

Problems of special biological or medical relevance are indicated with the symbol **BIO.**

Problems throughout the homework, labeled with the symbol **IP,** *integrate a conceptual question with a numerical problem.* Problems of this type, which stress the importance of reasoning from basic principles, show how conceptual insight and numerical calculation go hand in hand in physics. They afford students the opportunit...

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