Introduction

The 1B45 Mathematics course attempts to accommodate the changes in mathematical preparation afforded by A levels. These changes have become evident in the difficulties some of our students encounter in our physics and astronomy courses. Many of these difficulties stem from a loss of fluency in mathematics and associated manipulative skills. In physics and astronomy, laws are expressed mathematically, and mathematics is also needed to derive the consequences and interrelationships of these laws.

I urge you to accept the challenge of mastering this course because effort now will make it much easier to cope with the physics and astronomy courses. The challenge is as much to me as it is to you!!!

How are we to meet this challenge? Come to all the lectures and take a good set of notes. You must participate in the lectures and taking good notes is the start of this. I intend to develop the course in a reasonably logical and rigorous manner and to do many examples. The emphasis will be on the mathematics you will need for your physics and astronomy courses, and on acquiring fluency in mathematical manipulation. You really should go through your notes after every lecture, rewriting them as necessary, and going through everything I wrote down on the board.

Do the weekly problem sheets, normally given out in the Thursday lectures and collected in the Tuesday of the following week. Three of these problem sheets will be devoted to simple manipulative skills in differentiation, integration and vectors. You will be required to achieve more than 80% in each of the three, repeating them as necessary before you can complete the course.

Starting in a few weeks time there will be four bi-weekly two-hourly problem classes where groups of 15 - 20 students attempt a problem sheet. Demonstrators will circulate around to give help as needed. Again, don't be afraid to ask for help.

Half way through this term and in the last week of it there will be a class exam to tell me and you how well the course has gone. There is, of course, the final 1B45 exmination at the end of the academic year.

The book Mathematical Methods for Physics and Engineering , by K. F. Riley, M. P. Hobson and S. J. Bence, (3rd Edition - Cambridge), available from Dr Furniss, is a good text book for PHAS1245 and the follow on Maths courses PHAS1246 and PHAS2246 (2nd year).

Finally, do not underestimate this course. If you think you are familiar with most of the material, particularly early on in the course, persevere, there will be new material, and I will have some quite challenging problems to keep the most able of you happy! This course has been extremely successful with a good response from the students and a most satisfactory examination performance. Remember that a good effort now will make your physics and astronomy courses so much easier and much more fun!