Bøger af James B. Seaborn

This book is intended to provide a mathematical bridge from a general physics course to intermediate-level courses in classical mechanics, electricity and mag- netism, and quantum mechanics. The book begins with a short review of a few topics that should be familiar to the student from a general physics course. These examples will be used throughout the rest of the book to provide physical con- texts for introducing the mathematical applications. The next two chapters are devoted to making the student familiar with vector operations in algebra and cal- culus. Students will have already become acquainted with vectors in the general physics course. The notion of magnetic flux provides a physical connection with the integral theorems of vector calculus. A very short chapter on complex num- bers is sufficient to supply the needed background for the minor role played by complex numbers in the remainder of the text. Mathematical applications in in- termediate and advanced undergraduate courses in physics are often in the form of ordinary or partial differential equations. Ordinary differential equations are introduced in Chapter 5. The ubiquitous simple harmonic oscillator is used to il- lustrate the series method of solving an ordinary, linear, second-order differential equation. The one-dimensional, time-dependent SchrOdinger equation provides an illus- tration for solving a partial differential equation by the method of separation of variables in Chapter 6.

For the last eighteen years, I have been teaching an introductory course in as- trophysics. The course is intended for nonscience majors satisfying a general education requirement in natural science. It is a physics course with applications in astronomy. The only prerequisite is the high school mathematics required for ad- mission to the university. For a number of years, I used an astronomy text, which I supplemented with lecture notes on physics. There are many good astronomy texts available, but this was not a satisfactory state of affairs, since the course is a physics course. The students needed a physics text that focused on astronomical applications. Over the last few years, I have developed a text which my students have been using in manuscript form in this course. This book is an outgrowth of that effort. The purpose of the book is to develop the physics that describes the behavior of matter here on the earth and use it to try to understand the things that are seen in the heavens. Following a brief discussion of the history of astronomy from the Greeks through the Copernican Revolution, we begin to develop the physics needed to understand three important problems at a level accessible to undergraduate nonscience majors: (1) the solar system, (2) the structure and evolution of stars, and (3) the early universe. All ofthese are related to the fundamental problem of how matter and energy behave in space and time.

For the last eighteen years, I have been teaching an introductory course in as­ trophysics. The course is intended for nonscience majors satisfying a general education requirement in natural science. It is a physics course with applications in astronomy. The only prerequisite is the high school mathematics required for ad­ mission to the university. For a number of years, I used an astronomy text, which I supplemented with lecture notes on physics. There are many good astronomy texts available, but this was not a satisfactory state of affairs, since the course is a physics course. The students needed a physics text that focused on astronomical applications. Over the last few years, I have developed a text which my students have been using in manuscript form in this course. This book is an outgrowth of that effort. The purpose of the book is to develop the physics that describes the behavior of matter here on the earth and use it to try to understand the things that are seen in the heavens. Following a brief discussion of the history of astronomy from the Greeks through the Copernican Revolution, we begin to develop the physics needed to understand three important problems at a level accessible to undergraduate nonscience majors: (1) the solar system, (2) the structure and evolution of stars, and (3) the early universe. All ofthese are related to the fundamental problem of how matter and energy behave in space and time.

The book provides a bridge from courses in general physics to the intermediate-level courses in classical mechanics, electrodynamics and quantum mechanics. The author bases the mathematical discussions on specific physical problems to provide a basis for developing mathematical intuition.