Department of Mathematics Generic Syllabus
Boise State University Updated Fall 2006

Math 275
Multivariable and Vector Calculus
4 semester credits

Catalog Description

M 275 MULTIVARIABLE AND VECTOR CALCULUS (4-0-4) Vector algebra and geometry, functions of several variables, partial and directional derivatives, gradient, chain rule, optimization, multiple and iterated integrals. Parametric curves and surfaces, vector fields, divergence and curl, line and surface integrals, Green's, Stokes' and divergence theorems. Use of software such as Maple or Mathematica for visualization, exploration, and solution of ``real-world'' problems. PREREQ: M 175

Prerequisites

Second semester calculus.

Jurisdiction

This course is controlled by a departmental committee, whose members may or may not be teaching the course. All sections (there is usually only one) use the same text, which is chosen by the committee.

Learning Objectives

Upon completion of this course, the students will have made substantial progress in:

using the geometry of space: lines, planes, surfaces, and vectors in two and three dimensions to solve problems in mathematics and some elementary applications.
using the calculus of real-valued functions whose domains are sets in one, two or three dimensions and being able to explain why some theorems from one dimensional calculus fail in two or three dimensions.
applying the calculus of functions of several variables to a variety of elementary problems.
applying the calculus of vector-valued functions whose domains are sets in one, two or three dimensions to simple exercises.
acquiring a ``conceptual framework'' encompassing these topics and their potential applications.

1 Assessment of Learning Objectives

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts;

Periodic problem sets for homework serve both as learning and assessment tools. Classroom activities may vary depending on students' performances on homework assignments.
Problems given on in-class examinations are designed to give students the opportunity to demonstrate their ability to apply rules and formulae to the solution of simpler problems.
Instructor optional take-home examinations designed to evaluate the students ability to solve more complicated and time consuming problems. These problems give students the opportunity to demonstrate their ability to use technology to solve problems that are not amenable to simple analytic techniques.

Topics and Approximate Timeline


	Number of
Topic	Lectures
Functions of several variables (scalar fields)	6
Vectors, dot and cross product	3
Partial and directional derivatives, gradient, chain rules	7
Extrema and Optimization (including Lagrange Multipliers)	3
Multiple integrals, applications, change of variable	8
Parametric curves and surfaces	3
Vector fields and flow lines	2
Line integrals, conservative vector fields, Green's Theorem	4
Surface (flux) integrals	3
Divergence and the divergence theorem	3
Curl and Stokes' theorem	3
Total	45

Notice that this leaves 15 hours for work in the maple lab and for examinations and "slippage".

Text

The current text is Calculus, Multivariable, 5th Edition by James Stewart, Brooks/Cole Publishing. Other texts in recent years are Multivariable Calculus , Preliminary Edition, McCallum, Hughes-Hallet, Gleason. Wiley. Calculus with Analytic Geometry, Ellis and Gulick, Harcourt Brace and Jovanovich.

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion and sometimes small group activity.

Homework is an important part of the course. Part of the homework consists of computer-lab assignments completed outside of class. The Maple software environment is used especially to extend the students' experiences with three-dimensional graphics.

The exams may be given in class or take-home. The students are given a letter grade based on points earned. The points are typically available as:


Homework	200
Computer-lab work	100
Four exams	400
Final exam	200
Total	900

Letter grades are based on a scale in which 90% of the 900 possible points guarantees an A, 80% a B, 70% a C, 60% a D, and less an F, with the instructor having the discretion to adjust these cut-offs if warranted.

File translated from T_EX by T_TH, version 1.56.