PHYS 301 -- INTRODUCTION TO MATHEMATICAL PHYSICS -- Spring 2009

The UAF Catalog listing for PHYS 301: "Introduction to theoretical foundations of classical and modern physics. Includes calculus of vector fields, linear algebra and elementary tensor theory, complex analysis, ordinary linear differential equations, linear partial differential equations, Fourier analysis and probability. Physical applications include planetary motion, rotating bodies and inertia tensor, damped and driven harmonic oscillator, wave equation, Schrodinger's equation and diffusive systems."

In terms of the content of the textbook (which you must have and bring to classes), we will cover topics selected from Chapter 1 to 8 and 12 to 15 (i.e., we are skipping Chapter 9 to 11).  We will not cover all of any of the these chapters, due to the fact that we only have limited amount of time, not because other topics are not important. At the end of this syllabus is a tentative schedule which lists topics we plan to cover in more details. This is subject to change. So you should check frequently the online version of this page: http://www.gi.alaska.edu/~chungsangng/phys301/phys301.html.

Note: we will not go over Chapter one (Power Series) in details in class, since you should have learned about similar subject before. However, we will use materials covered there in later Chapters. Therefore, you should read it through and ask for help if you have questions.

The main goal of this course is to introduce you to the mathematical tools that you will need in your study of the upper division courses in the Physics major. Of course these mathematical tools have much broader application in many technical fields other than physics, e.g, engineering, industrial research/development, and even economics/finances. A more general goal is that you will learn how to look up methods of using these (and other) mathematical tools (through mathematical references, handbooks, or tables) when you are facing a need in the future, even if you might have forgotten details you have learned in this course. This course, and its companion course PHYS 220 "Introduction to Computational Physics", are crucial prerequisites for the rest of the undergraduate Physics curriculum.

You must have a copy of the textbook: Mathematical Methods in the Physical Sciences, 3rd edition by M. Boas, John Wiley & Sons, 2005 (ISBN 978-0-471-19826-0). It is very important that you read the chapter(s) before you come to the lecture that covers that chapter(s). Please refer to the schedule below (subject to change) for such reading assignments. You should bring your textbook to the Lectures and Recitations. The publisher provides a listing of errata for the text.

You will find it extremely useful to have some mathematical references, handbooks, or tables, e.g., table of integrals. An important part of the course is to become familiar with how to use these tools. There are many options available from the Internet, but you should be cautious about the accuracy of information obtained there. One recommendation is Abramowitz and Stegun: Handbook of Mathematical Functions, which can be downloaded freely. Another one is Gradshteyn and Rhyzik.

The class is 4 credits, of which 3 hours per week are devoted to lecture. Based on the reading schedule listed below, you should have looked at the material in the text before coming to each day's lecture. I will not have time to read through the text, but will only highlight those points that are important or difficult. You must cover the rest of the text and ask for help if you encounter difficulties. I reserve the right to assign homework or exam questions over materials listed in Reading Assignments, even if it was not covered explicitly in lecture.

The remaining 1 hour per week of the class is devoted to recitation. The recitation is scheduled for Tuesday morning, and based on that, the homework is due on Friday (at the beginning of class; late homework will not be accepted). During the recitation, I will present examples and additional material to supplement the lectures, hints and assistance for the coming homework, and solutions to selected past homework. You will also be asked to do some in class questions, either by yourself, or in small group.

Note: some lecture notes will be available for download via the course home page (http://www.gi.alaska.edu/~chungsangng/phys301/phys301.html) by clicking at the dates of the lectures in the schedule. These notes are not to replace the lectures themselves or the textbooks

Doing homework is key to doing well in this class.  As the author of the textbook said in "To The Student": The only way to learn to solve problems is to solve problems. There will be one homework set assigned each week, usually on Fridays, and is usually due in the following Friday before class.  However, you should work on your homework as early as possible before a deadline so that you can have time to ask for help if you encounter difficulties in solving these problems. Late homework will not be accepted.

To emphasize the importance of doing homework, homework grade will count towards 40% of the total grade of the course, excluding the assignment with the lowest grade. 

Most homework questions will be assigned from those questions in the textbook that do not have answers listed in the back. However, you should try to work on your own other questions in the textbook that are similar to those assigned in the home work and have answers listed. This will allow you to check if you know the method that can give correct result. Your submission of any homework problem cannot be simply a one-line statement of the answer. You need to show steps of how you used the method leading to that answer. I will grade the homework based on the method used, as well as the answer. Therefore, you should submit your partially finished work. This will help you getting partial credit, and let me identify your difficulties. Also, your work should be clean and clear enough for me to understand.

While it is good for you to have discussion with classmates or search the Internet for additional information, your submitted homework should be of your own, but not a direct copy from another source. Keep in mind that you will be required to do similar questions on your own during exams. In addition, it is against the UAF Honor Code to misrepresent work which is not your own. Plagiarism on homework or on an exam will result in a failing grade.

Solutions to the homework problems will be emailed to you after the due date. Therefore, late homework will not be accepted. The homework assignments will be given in class, and on the course website (click on links within the Schedule).

There will be one one-hour in-class midterm exam on Friday March 20th, and a two-hour final exam on Wednesday May 6th from 1 to 3 PM. Both exams are open textbook and open notes. You may also bring your mathematical handbooks or tables. Calculators, computers, and communication devices are not allowed. The purpose for the open book policy in exams is to encourage you to concentrate on learning the methods and techniques of solving problems, rather than memorizing formula. You should also get familiar with how to look up information in your textbook, handbooks, or tables. Special or unusual formula or integrals essential to a particular question will also be written down for that question and so there is no real advantage in bringing "better" handbooks. Midterm exam counts towards 20% of the total grade. The final exam counts towards 40% of the total grade. You must not miss the midterm exam and the Final Exam (except for documented illness or family emergency ).

Some questions in the exams will be similar to those you have seen in homework. Thus, it is important to review homework sets and solutions before the exams. Exam questions will be graded based on the method used, as well as the answer. Therefore, you should write down explicitly and clearly step by step how you come up with your answers. This will help you getting partial credit.

My office hours are 3:20 PM - 4:20 PM on Monday and Wednesday, 10:50 AM - 11:50 AM on Tuesday, and 1:10 PM - 2:10 PM on Friday. I will be at Reichardt 108 during these office hours. Canceled office hours will be announced in class or by email. If you need to see me outside these office hours, please set up a time by appointment to come to my office at Elvey 706E. These are hours set aside especially to help you - do not feel like you are imposing or cheating by coming in. If you have problems that need immediate attention, please send me an e-mail or give me a call at my office phone number.

I have set up a home page for the course: http://www.gi.alaska.edu/~chungsangng/phys301/phys301.html. I may put additional materials that may be helpful to you later on. So, please come back often, especially to check any changes in the schedule. The UAF Blackboard site for this course will be made available to students, but will not be used to provide communication about this course.

The Physics Department will work with the Office of Disabilities Services (203 WHIT, 474-7043) to provide reasonable accommodation to students with disabilities.