MA387:  Mathematical Analysis I

 Spring 2009.

A one-semester course providing a rigorous introduction to the calculus of a single variable.  The course is designed to introduce the student to the foundations of the calculus necessary for advanced undergraduate and graduate studies in applied mathematics and engineering.  Course coverage includes a treatment of the structure of the real number system, sequences, continuous functions, and differentiation.

Our textbook is by David Bressoud and it entitled A Radical Approach to Real Analysis, second edition. Be sure to check out this link, for it contains additional material and Mathematica code for the exercises. This will save you a lot of typing.

Day 1, Jan. 10. Read the preface and section 1.1. 

Section 1.1

• Exercise 1-1-5
• Exercise 1-1-6 (i.e., exercise 6 from section 1.1)
• Exercise 1-2-2 shows how to graph partial sums of certain series.

Here is how to invert the arcsine series and get the sine series.

References:

1. Darrigol, Olivier, "The acoustic origins of harmonic analysis," Archive for History of Exact Sciences, July 2007, Vol. 61, Issue 4, pp. 343-424. Journal available online.
2. Grattan-Guinness, Ivor, Joseph Fourier, 1768-1830; a survey of his life and work, based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807, MIT Press 1972. Circulating Books: QA29.F68 G7.
3.  Herivel, John, Joseph Fourier : the man and the physicist, Oxford : Clarendon Press, 1975. Circulating Books: QC16.F56 H3.
   

Here are a few things that I think you might find interesting and useful:

• Hints For Success that I have encouraged students to follow for many years.
• Read your book
• To learn something about my background you may wish to consult my automathography, which was written in August of 1998 when I joined the USMA faculty.
• My Teaching Philosophy.
• A note On Standards in the MA205 FSE.
• Section Marcher Duties.
• Why Army Officers Need to Know Mathematics
• The Conic Sections
• Riemann and the Integral
• An anecdote about exams
• A Sonnet to "Analytical," being a piece of cadet doggerel written before an exam.
• The Olivier Models were used to teach descriptive geometry at USMA in the nineteenth century. These are the string models in large cases on the second floor of Thayer Hall. I have begun to compile more information about them.
•  My primary research interest is in the history of mathematics, especially the history of the calculus. One of my research plans is to write a history of the Department of Mathematical Sciences at West Point. So far I have collected a good deal of information about the Mathematics Teachers at USMA.

An interesting mathematical event that takes place each spring, and is designed specifically for undergraduates, is the Hudson Valley Undergraduate Mathematics Conference. I attended twice in the past several years with cadets and had a wonderful time. 

The easiest way to contact me is via email at  Fred-Rickey@usma.edu . You can also reach me by phone at 938-4010 or stop in my office in room 251 Thayer Hall.