# Mathematics for College Physics

## Biman Das

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This book is designed to help readers get up to speed quickly on the mathematical concepts and tools needed to solve basic physics problems. Instead of a rigorous development of the concepts of mathematics (as is found in a typical math book), it describes the various mathematical concepts and tools and their direct use in physics. Almost all sections end with worked-out examples and exercises taken directly from basic physics. Algebra: Dealing with Numbers and Equations in Physics. Trigonometry: A Powerful Tool to Solve-Real-World Problems. Geometry: Dealing with Shapes and Plots. Calculus: A Way of Probing the Changing World. Vectors: Tracking the Direction of a Change. Probability and Statistics: Analysis of Data and Predicting Future from the Present. For anyone needing a quick review of math for physics applications.

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From the Back Cover:

Designed for concurrent self-study or remedial math work for students in introductory courses, this text is ideal for students who find themselves unable to keep pace because of a lack of familiarity with necessary mathematical tools. It not only shows them clearly how mathematics is directly applied to physics, but discusses math anxiety in general and how to overcome it. Instead of a rigorous development of the concepts of mathematics (as is found in a typical math book), the text describes the various mathematical concepts and tools (including algebra, trigonometry, geometry, vectors, and statistics) and their direct use in solving physics problems. Almost all sections end with worked-out examples and exercises directly from introductory physics.

This book is written for students who plan to take or who are presently taking an algebra-trigonometry-based physics course. The book will develop mathematical skill, provide the students with the competence to use mathematics, and serve as a mathematical resource. Students will find how mathematics is directly applied to physics. Students who have not recently taken a course that required mathematical skill often find themselves unable to keep pace in an introductory physics course because they are not familiar with the necessary mathematical tools. This book is written with these students in mind. Students taking other physics and science courses will also find the book useful.

The book consists of seven chapters. Chapter 1 introduces students to physics and mathematics and discusses the role of mathematics in physics. It also discusses how to deal with the math anxiety that many students have, as well as how to develop good study habits. Chapter 2 describes scientific notation, units, and dimension of physical quantities. Chapters 3 through 7 describe the mathematical concepts and tools including algebra, geometry, trigonometry, vector, and statistics, with selected examples and real-world problems. Chapter 7 covers statistics and elaborates on the techniques of analyzing experimental data; it provides tips on how to be successful in a physics laboratory.

The book emphasizes primarily the use of mathematical techniques and mathematical concepts in physics and does not go into their rigorous developments. Wherever possible, I have included examples and problems from physics so that students see how the concept of mathematics is directly applied to physics. The book is written so that students can study it to develop mathematical skills and can practice solving problems. There are worked-out examples and exercises in almost every section. The book can also be used as a text for a one-to two-credit course (dependent upon the depth of the coverage), a remedial mathematics course, or a physics recitation course for students taking an introductory physics course. Both the publisher and I realize the necessity of the book for introductory physics students.

I would like to thank Dr. David Reid (East Michigan University), Dr. Ronald J. Bieniek (University of Missouri-Rolla), Dr. Anthony Pitucco (Pima Community College), Dr. Jenny Quan (Pasadena City College) and Dr. Dennis Rioux (University of WisconsinOshkosh) for their reviews and suggestions. Special thanks are due to Dr. Michael B. Ottinger (Missouri Western State College) for his detailed comments and suggestions for improvements. I thank Mr. Christian Botting, Associate Editor, Physics and Astronomy, Prentice Hall, for his constant support and cooperation throughout the entire process. I also thank Donna Young, Production Editor, Prentice Hall, for her cooperation. I thank my wife Indrani Das and my daughters Debapria Das and Deea Das for their cooperation and support without which I could not get any free time to write the book. I would appreciate any constructive comments about the book.

To the Students

The primary purpose of this book is to develop mathematical skills that will allow you to concentrate on the physics in a physics course. You should find the book useful in other science courses that involve problem solving, and you can use the book as a mathematics resource book. The book is not meant to be a substitute for standard mathematics courses that may be prerequisites for an introductory physics course. The mathematics discussed is comparable to what you will find in a typical mathematics text. The emphasis is on enhancing those mathematical skills frequently used in a physics course. One objective of the book is to show you how the concepts of mathematics are directly applied and related to physics and real-world problems.

For many of you, college level physics is different from most other courses. The emphasis is on understanding the physical concepts, deriving the physical laws or principles using mathematics, and applying this knowledge in solving a wide range of problems. There may be several obstacles to understanding physics and mastering problem solving. However, the primary factor that leads to success in physics and problem solving is the competence to use mathematics with ease and accuracy. My hope is that the book will make you stronger in mathematics so that your learning experience in physics will be beautiful and rewarding. The beauty of physics cannot be enjoyed if you are distracted and inhibited by a less-than-adequate mastery of basic mathematical skills.

For your convenience, I have included important conversion factors, a list of fundamental constants, useful data, and other information in the appendices. I have used boxes throughout the book to draw your attention to important concepts or formulas. I have also used the boxes to inform you of students' common mistakes.

Read Chapter 1 to learn about fun with physics and mathematics. Learn also how to develop good study habits and how to deal with math anxiety. Then begin Chapter 2. Good luck!

Biman Das

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