<p>Calculus III (Multivariable Calculus) is the third course in our three-course calculus sequence. Successful completion of Calculus II (Math 22 or Math 23) is a prerequisite for Calculus III. The course topics include an introduction to vectors and coordinate systems for three-dimensional space; vector functions, with a discussion of derivatives, velocity, acceleration, arc length and curvature; functions of several variables, where we extend the basic ideas of differential calculus to these functions; the concept of the definite integral is extended to double and triple integrals, with applications such as volume, mass and centroids, while introducing two new coordinate systems in three-dimensional space (cylindrical coordinates and spherical coordinates); a study of vector fields, line integrals and surface integrals, leading to a discussion of Stokes? Theorem and the Divergence Theorem. Topics will be presented with a level of depth and rigor appropriate for students pursuing degrees in technical fields such as mathematics, statistics, engineering, or the physical sciences. The computer algebra system Mathematica will be used throughout the course.</p> <p>Required Course Materials: You will need the paperback or eBook version of the required text, and an access card for Enhanced WebAssign online homework. If you took Math 21 and/or Math 22 at UVM during the 2011 ? 2012 academic year, this is the same text that you used, and your WebAssign access code should still be active. If you do not already have the text and WebAssign access, choose one of the following options.</p> <p>Option 1: Enhanced WebAssign with eBook Access Card for Multi Term Math and Science. ISBN 0-538-73807-3 <br />This includes a homework access card and online access to the eBook.</p> <p>Option 2: Calculus: Early Transcendentals, Hybrid Edition (with Enhanced WebAssign with eBook Access Card for Multi Term Math and Science), 7th Edition, Stewart. ISBN 1-111-42668-6 <br />This includes a homework access card and online access to the eBook, plus a paperback textbook.</p> <p>Note About Used Books: If you purchase a used copy of the paperback textbook, you will need to separately purchase an access code for Enhanced WebAssign with eBook (ISBN 0-538-73807-3) or Enhanced WebAssign without eBook (ISBN 0-538-73811-1). This can be easily purchased online from within WebAssign after class begins.</p> <p>Software: The Mathematica software used in the course is provided by UVM; you do not need to purchase it. You may install Mathematica on your own computer free of charge under UVM?s site license. Mathematica is also available for use in various computer labs and classrooms on campus.</p>

Students are assumed to know the content of Mathematics 22. There will be regular assignments which will be completed on line using WebAssign. In addition, students will be expected to complete some assignments utilizing Mathematica.

The grade will be based on (1) the quiz average, (2) the midterm examination, (3) the final examination and (4) the assignment average. The quiz average will count as one score, the midterm will count as two score and the final will count as two scores. Of these five scores, the lowest (or one of the lowest) will be dropped . The remaining four scores and the assignment score will determine the course grade, with all component scores weighted equally. The assignment score will be an average of the WebAssign scores and the scores on the Mathematica assignments.