Math 21-259Calculus in Three DimensionsSyllabus, Spring 2019Times and Places:MWF 8:30-10:20DH A302MWF 12:30-1:20DH A302Instructor:Dr. Greggo M. JohnsonOffice:Wean Hall 8122Phone:412-268-1504E-mail:[email protected]Class webpage:Office Hours:M 1:30pm-2:30pm, Tu 12:00pm-1:00pm, W 1:30pm-2:30pm, or by appoint-mentRecommended Text.James Stewart.Calculus:Early Transcendentals, 8th Edition,Cengage Learning, 2016. ISBN-10: 1-285-74155-2, ISBN-13: 978-1-285-74155-0Course Content. Math 21-259 is the final course in the calculus sequence. We will coversuch topics as vectors, vector-valued functions, partial differentiation, multiple integrals,line integrals and surface integrals, as well as various fundamental calculus theorems. Thecourse covers chapters 12 through 16 of the textbook (see attached schedule). The studentis assumed to be capable and versed in the standard Calculus I and II topics including, butnot limited to, limits, differentiation, Riemann sums, techniques of integration, techniquesof approximations, and applications of differentiation and integration. Due to the amountof material necessary to cover, this course proceeds at a very fast pace. Please don’t beafraid to stop me and ask questions.Learning Objectives. Upon successful completion of this course, students should be ableto1. Find dot products, cross products, and vector projections.2. Understand and analyze vector-valued functions, including being able to parametrizebasic curves, integrate and differentiate vector-valued functions, find arc length, andcurvature.3. Differentiate, optimize, and approximate functions of several variables. This includesfinding limits of functions of several variables, taking partial derivatives, finding tan-gent planes, finding directional derivatives, and using Lagrange multipliers.4. Set up and evaluate double and triple integrals.This includes transformations topolar, cylindrical, and spherical coordinates, as well as general transformations. In

addition, students should be able to derive double and triple integrals from Riemannsums, and students should be able to find centers of mass for 2-D and 3-D regions.5. Set up and compute line and surface integrals, including being able to implementGreen’s Theorem, The Fundamental Theorem of Line Integrals, Divergence Theorem,and Stoke’s Theorem.Homework. Homework is essential to understanding the material covered in this course.There will be both online homework and written homework each week. The online home-work system is a *FREE* program that I have used before with much success.