Course Description

Students pursuing advanced study in physics and other physical sciences (astronomy/astrophysics, meteorology, geophysics) will encounter a series of problems whose solutions will require advanced and sophisticated mathematical tools. This course seeks to provide students with the necessary knowledge and experience to tackle the sorts of problems they will face in their future studies.

I strongly recommend that all students purchase both books for the course. The text by Boas is required, and Griffiths is the book that is used in Phys 351 (electrodynamics).

We will begin the course with a study of vector calculus (Boas Ch. 6; Griffiths Ch. 1), although it will be Griffiths. treatment we will follow more closely. Additionally, we will establish in class how Einstein summation notation can be used to prove vector identities much more elegantly than the techniques suggested in either Boas or Griffiths.

Our next topic will be orthogonal curvilinear coordinates, which is spread across many sections of the texts. I will synthesize these topics in class, as well as provide more detailed explanations and examples than occur in either text.

Preparatory to an extensive study of differential equations, we will cover Fourier series (Boas Ch. 7 and allusions in Griffiths Ch. 3). The second half of the course will focus solution of differential equations, both ordinary and partial, using selected sections of Chapters 8,12, and 13 in Boas and portions of Ch 3. in Griffiths.

The projected outcome of this course if for each of you to be prepared for the mathematics you will encounter in higher level physics courses, and also be prepared to study other sorts of differential equations (and special functions) on your own.

As noted above, the prerequisite for this course is a minimum grade of C- in Math 263 or equivalent. Students lacking this prerequisite cannot (and should not) remain in the class.

GRADING AND POLICIES

Your grade in the course will be determined by your scores on each of two one hour exams, homeworks, and a final exam.

Hour exams will be given on Wed. Feb 28 and on Friday, April 20. Each exam will cover the material presented in that half of the course (for purposes of continuity, the second hour exam may cover some material from the first half of the course). It is my expectation that students will take the exams on the day they are given. Exams will be rescheduled only for the following reasons: a medical situation requiring physician's care; death of a member of your immediate family; an unavoidable court date; religious holiday which prohibits normal activity (such as attending class); representing Loyola in an official capacity requiring your absence from campus (such as Model UN, Debate Team, intercollegiate athletics). In all cases, the student must provide written and documentable evidence as soon as possible. Travel is not an acceptable reason to miss an exam, unless that travel occurs pursuant to one of the five reasons mentioned directly above.

Homeworks will be given frequently (I anticipate ten or more homework assignments during the semester). While it is allowable and even advisable to work in groups on homeworks, the homework you submit to me must be the result of your own independent work. This means you cannot copy anyone else's solution, nor can you write down a group solution and use that copy for your submission. Homeworks must be submitted in class on the day they are due; since I will post solutions right after class, homeworks submitted late will earn no credit. (We will make alternate arrangements if you are unable to submit homework due to one of the reasons given in the section on hour exams.)

The final exam will cover all material presented in the course and will take place in this room on Saturday (sorry folks) May 5 at 1:00-3:00.

Final grades will be computed according to:

HOMEWORK FORMAT

As already noted, homework will be a frequent and important component of this course. To enable me to grade all of your homeworks and return them to you in a timely manner (I try mightily to return all homeworks the following class period), I ask that you follow this format for all homework submissions:

1) All homework assignments must be stapled (not paper clipped, not pages folded over) in the upper left hand corner. 2) All writing must be done on only one side of each sheet. 3) Homeworks must always show clearly how you arrive at your solution; as you have learned in previous physics and math courses, your method of solution is far more telling than your final answer. 4) Homeworks must be legible; if I cannot read or follow your work, I cannot grade it.

I will not be able to give any credit for illegible homework, and will deduct 20% from any homeworks not conforming to conditions 1) and 2) above.

ACADEMIC HONESTY

Academic honesty is the cornerstone of any university and of the way in which scientists do research. Accordingly, I will hold you to the standards of academic honesty established by Loyola. Failure to meet these standards will have serious repercussions: Any instance of academic dishonesty on an exam (specifically but not exclusively copying from another student, using "crib" notes) will result in an "F" in the course and I will send a report to the Dean's Office describing the situation. Submitting homework that is not the result of your own independent work constitutes academic dishonesty. The first instance of academic dishonesty on homework will result in a zero on that homework; the second instance will yield a grade of F for the course. In all cases I will submit a report with copies of the material to the Dean's Office.