Applied Physics: Concepts into Practice (with CD-ROM)
Editorial Reviews
Book Info
Develops mathematical ways of looking at physics to enable the reader to understand physics equations. Includes cross-references to Math Review and Calculator Usage appendices, key concepts summary of terminology, and more. DLC: Physics.
From the Inside Flap
Preface
Applied Physics: Concepts into Practice is intended for students enrolled in engineering technology, engineering, and medical degree programs. Students should have a basic knowledge of algebra, geometry, and trigonometry at the high school level. With this math background, students should be able to understand everything in the book. The text is intended for use in a two-semester sequence. For the first semester, Parts 1 and 2 cover mechanics and thermodynamics. For the second semester, Parts 3, 4, and 5 discuss electromagnetics, optics, and some modern physics.
Physics is the study of the forces in nature and how those forces interact with matter. Because these interactions can often be stated in a precise mathematical form, physics involves much use of mathematical modeling. The formulation of physical laws in a mathematical framework implies that a prerequisite of a serious study of physics is a certain fluency with mathematics. However, it is not necessary that students have such fluency before they begin the study of physics. Rather, the mathematical fluency can be developed along with the physical concepts.
In Applied Physics, mathematics is used as a language to describe the workings of nature, in contrast to being used as a number grinder where raw data are reduced to numerical answers that give no sense of perspective. Often in problem solving, physical concepts are used only to initially set up a problem, and then the problem becomes essentially one of mathematics. However, in this text, the internal consistency of the mathematics takes the problem to its final answer, which has a very real physical significance. Mathematical formalism is minimal, and a common-sense approach to mathematical methods is employed. The mathematics is "bootstrapped" along with the physics. By studying the text, students will naturally come to be able to "speak" mathematics with a certain degree of fluency.
In this way, I have gone beyond the mathematical limitations that an algebra-based text often imposes upon itself. I wrote Applied Physics because I could not find a textbook that integrated the physics and math well at the applied physics level. The mathematical approach for this kind of text is new. But in giving this book the mathematical continuity such a text so sorely needs, I have remained within the prerequisite student math background of only algebra, trigonometry, and geometry. With this background, many of the basic principles of higher math can be developed in a common sense way: on an as-needed basis when the physical concepts require it. The physics drives the math, not vice versa. A physicist, Sir Isaac Newton, invented the mathematical discipline known as calculus because the deeper mathematical perspective that calculus provided was necessary for a deeper physical understanding of the universe. Role of Derivations
In my teaching experience, I've noticed that students have the most difficulty with problem solving in properly interpreting a problem. Identifying a problem's context is crucial to its solution. If students know where an equation comes from, they know what situation the equation describes and what the equation is capable of solving. They also know what a particular equation cannot do. Without the proper context, all equations are alike, and the students cannot see the forest for the trees. Therefore, derivations are given for most equations used in this text. By presenting the derivations, the text effectively demonstrates the use of mathematics as a language and modeling tool. Thus, a sense of perspective as to the physical concept can be attained. Problem Solving
My advice to students is to do problems, work problems, and then do some more problems! In doing problems, students must struggle with the theory and in so doing gradually become familiar with it as they set up a problem, review it, and determine how to solve it. Answers are provided for each problem, giving students a goal to reach for. A great deal of material must be included in two semesters, and thus a fast pace is required. Therefore, the problems at the end of each chapter have been kept to a number that could reasonably be attempted during the time period allotted for each chapter. More difficult problems are indicated by an asterisk (*) before the problem number. There are very few "plug-and-chug" problems in this text. However, the book is sufficiently complete that students will not have to refer to an outside text to solve any of the problems.
Applied Physics gives students an opportunity to understand physics, in contrast to simply being exposed to it. Obtaining the correct answer for an exercise does not necessarily mean that the solver has any insight into the physical concept being investigated. For example, computers can crank numbers, but computers have absolutely no sense of perspective as to the nature of a given problem. Traveling the path to a correct answer is a significant learning experience for students. Their reward is a correct answer. The answers to the problems in Applied Physics are, in most cases, not nice round numbers because the world seldom operates in nice round numbers (take p, for instance). If the answer that a student obtains for a certain problem is essentially the same one given in the text, then the answer is probably correct. A student's answer may vary from the one given in the text because of round-off errors. Students shouldn't worry if their answers disagree slightly with the answers in the book. The path to an answer is what is important, not the number of decimal places to which the answer is carried out. Units and Dimensional Analysis
Although I haven't devoted any space specifically to units and dimensional analysis, Appendix C includes a table of common symbols, dimensions, and units. Units are carried along in all of the examples. I feel that dimensional analysis is a contextual subject and thus can be taught most effectively by including appropriate units in each example. An answer for a given problem is usually not just a number, but a number that has some physical meaning associated with it. That physical meaning is usually assigned a name, such as a force in newtons or a mass in kilograms. In solving the problems, students are required to set up their own equations for a solution. The final equation should have the appropriate units. If, for example, the answer is energy in joules, the final equation should have dimensions of energy and not, say, momentum. If the final equation is dimensionally incorrect, then there is something wrong with the derivation.
Dimensional analysis is not a subject in its own right, but rather an aid to obtaining a proper perspective of a physical concept. Dimensional analysis also can be a big help in initially learning the language of mathematics. Often it is the only way that students know, in beginning their study of physics, whether or not the end equation will solve the problem. Dimensional analysis is ever-present in this book, but seldom directly focused upon. Applying the Approach to the Real-World Classroom
Through several years of teaching at IUPUI, I have successfully taught introductory applied physics students using the approach of integrating physics and math-in both the classroom and the lab. The approach that math and physics go hand in hand is gaining ground. A nationwide workshop, called the CPU (Constructing Physics Understanding) Project, was recently conducted for high school teachers. The workshop was supported by the National Science Foundation and was funded by an Eisenhower Grant. In the workshop, laboratory-based elicitation exercises were used to develop the physical concepts being studied, and direct experience was used to debunk tightly held initial misconceptions about physics. In the force and motion studies, the laboratory equipment included motion carts and inclined planes as well as ultrasonic motion sensors interfaced to computers that, with the appropriate software, gave real-time plots of displacement, velocity, and acceleration versus time. Teachers in the role of students could obtain a direct correlation between the motion studied and the shape of a graph. Later teachers used these same graphs, coupled with the equation of a straight line and the ability to find the area inside simple geometric shapes such as a rectangle or a right triangle, to derive the four equations of motion. They learned that a continuum of ideas leads from the basic concept of motion to the mathematical representation of that motion on a graph to the derivation of equations describing that motion. The integration of math and physics and the continuum between the two is one of the guiding philosophies of this book.
Also in the workshop, the propagation of light was studied in optics. The equipment used was a small flashlight with a grain-of-wheat bulb as a point source of light. The light was shone on a small, solid square template, and the shadow was observed. Up to four flashlights were stacked one upon another, and the shadow went from a dark square through four steps to
Applied Physics: Concepts into Practice (with CD-ROM)
Applied Physics: Concepts into Practice (with CD-ROM),Gregory S. Romine,Prentice Hall,0135324661,Physics,Physics (General),Science,Science/Mathematics,Science / Physics
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