Logistics (tentative):

• Course: MTH MAS 4156-001, ref # 82479
• Prerequisites: Linear Algebra (MAS 3105) and either Calculus III (MAC 2313) or Engineering Calculus III (MAC 2283)
• Time & Place: TR 9:30 - 11:20 in PHY 013
• Instructor: Gregory McColm
• Office: PHY 338 (inside Suite PHY 342)
• Hourse: MW 2 - 2:50 & TR 11:30 - 12:15
• Phone: (813) 974-9550
• E-mail: mccolm@cas.usf.edu
• URL: http://www.math.usf.edu/~mccolm
• Text: Calculus: Early Transcendental Functions, 4th ed., by Larson, Hostetler & Edwards, and a booklet. For complications on purchasing the text, see below.

The text will be the same one we've been using at USF during the last few years for Calculus I, II, and III, and for Engineering Calculus I, II, and III. If you still have that text from your calculus course here at USF, keep it. If you do not have this text, you will need to get one, and the difficulty is that there are many versions of this book, with many ISBN numbers and publication dates: many versions of this book were custom published, and the ISBN number refers to the custom publication, while the publication date refers to the date of the custom publication. What you want is a copy of the 4th edition of Calculus: Early Transcendental Functions by Ron Larson, Robert Hostetler, and Bruce Edwards,published by Houghton-Mifflin; the original version of the 4th edition was published in 2006, but there have been many custom publications since then. What you want is any version of the 4th edition that contains the following:

• Chapters 9 – 15. This is the material we will be covering.
• Appendices A & B.
• The index.
• And if you so desire, the answers to odd-numbered exercises in chapters 9 – 15.

• You may notice that the prices for used copies go up & down -- one day, there's one available for $ 60, another the cheapest is $ 90. There is a whole buying-and-selling cycle between now and the end of August, so you can afford to wait a month or so for a decently priced used copy to drift by.
• You may also notice that there are a number of really cheap copies of the Third edition for sale. There are minor omissions from the Third edition, which can be irritating, but the Third edition is usable for this course. If you do get the third edition, you must make sure that whatever version you purchase has the material, which is in differently labeled chapters and appendices, namely:
  • Chapters 8 - 14.
  • Appendices B & C.
  • The index.
  • And if you so desire, the answers to odd-numbered exercises in chapters 8 - 14.
  Warning: The first and second editions are not recommended for this course.

This course is essentially a continuation of the Calculus I, II, III sequence. Like the previous courses, this course covers mathematics that was developed primarily to deal with contemporary physics problems. Calculus I covers mathematics designed to deal with linear mechanics (e.g., falling balls) and Calculus III covers mathematics designed to deal with celestial mechanics (e.g., planets orbiting the sun); these are issues that mathematical physics had great success with in the Seventeenth and Eighteenth centuries. Nineteenth century physicists from Gauss to Maxwell worked on electricity and magnetism, and much of the calculus developed in that century was intended as tools for dealing with the physics of electromagnetism. Many other applications have appeared since then, and this is the mathematics that we will cover this semester.

Specifically, we will cover (from the text):

• A review of Calculus III to get up to speed. We will first zoom through Chapters 10, 11 and 12.
• But then in Chapter 13, we will start going into some subjects in greater detail, like limits and continuity (this course will be more proof-oriented than Calculus III). The review part continues into Chapter 14, although we will be using increasing amounts of material from the booklet in order to get a more theoretical view of the subject.
• The body of the course consists of the second half of Chapter 14, and all of Chapter 15.

• This course could roughly be described as the mathematics developed during the Nineteenth century in order to deal with electrodynamics, in particular with Maxwell's equations. So our practical goal is to cover and understand Green's Theorem, Gauss's Divergence Theorem, and Stokes' Theorem, and then understand what Maxwell's equations are saying.
• This course is also the (first) half of Advanced Calculus, the other half being Intermediate Analysis. So we will be spending time understanding definitions, theorems, and proofs.