After teaching this for four consecutive years, from the 06-07 to the 09-10 school years, I now no longer teach this course. This has been replaced by the calculus curriculum for the magnet school, “Magnet Calculus.” Much of this course will be included in Magnet Calculus II.
The textbook I used for this course is the comprehensive Advanced Calculus, fifth edition, by Wilfred Kaplan. I like this book mainly because of the short but comprehensive treatment of linear algebra in addition to the rigorous development of multivariable calculus. I feel the linear algebra is just as important as the calculus; however, many calculus texts simply do not give linear algebra a fair treatment (or any treatment at all).
I spend half a semester on linear algebra concepts before introducing any calculus.
Posted here are my course notes. These are very rough but do provide a fairly accurate picture of what is discussed each day. I base my lectures on the material in the textbook. The teaching of this course is approached as closely as possible to a college style lecture experience.
Although this course is on the state approved list of mathematics courses, there are no stated objectives or standards. This allowed me to structure the course how I saw fit, and to choose any textbook I wanted.
With the introduction of the Georgia Performance Standards, it was necessary to write standards for this course in order to continue offering it. Since I was not going to let this content fade away, I wrote the standards. They are approved and posted on the Department of Education website.
Tests from previous years
Below are some sample tests that I distribute to help students prepare for the test. These have proved very beneficial. This is chiefly because this course is the first time my students are asked to prove theorems on a test.