MATH 242 : Multivariable and Vector Calculus

Credits: 4

Course Description: Differential and integral calculus of functions of several variables and of vector fields. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional derivatives, optimization in several variables; multiple integrals, iterated integrals, change of coordinates, Jacobians, general substitution rule; curves and surfaces, parametrizations, line integrals, surface integrals; gradient, circulation, flux, divergence; conservative, solenoidal vector fields; scalar, vector potential; Green, Gauss, and Stokes theorems.

Pre-Requisites: MATH 141.

Comments: Because MATH 242 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. No student receives graduation credit for MATH 240 if it is taken after successful completion of MATH 242. Students may take MATH 242 after MATH 240 only with the explicit permission of the Department and then only for one credit.

Topics:

Chapter 13:: 13.1 Three-Dimensional Coordinate Systems.
13.2 Vectors.
13.3 The Dot Product.
13.4 The Cross Product.
13.5 Equations of Lines and Planes.
13.6 Cylinders and Quadric Surfaces.
Chapter 14:: 14.1 Vector Functions and Space Curves.
14.2 Derivatives and Integrals of Vector Functions.
14.3 Arc Length and Curvature.
14.4 Motion in Space.
Chapter 15:: 15.1 Functions of Several Variables.
15.2 Limits and Continuity.
15.3 Partial Derivatives.
15.4 Tangent Planes and Linear Approximations.
15.5 The Chain Rule.
15.6 Directional Derivatives and the Gradient Vector.
15.7 Maximum and Minimum Values.
15.8 Lagrange Multipliers.
Chapter 16:: 16.1 Double Integrals over Rectangles.
16.2 Iterated Integrals.
16.3 Double Integrals over General Regions.
16.4 Double Integrals in Polar Coordinates.
16.5 Applications of Double Integrals.
16.6 Triple Integrals.
16.7 Triple Integrals in Cylindrical Coordinates.
16.8 Triple Integrals in Spherical Coordinates.
16.9 Change of Variables in Multiple Integrals.
Chapter 17:: 17.1 Vector Fields.
17.2 Line Integrals.
17.3 The Fundamental Theorem for Line Integrals.
17.4 Green's Theorem.
17.5 Curl and Divergence.
17.6 Parametric Surfaces.
17.7 Surface Integrals.
17.8 Stoke's Theorem.
17.9 The Divergence Theorem.

Spring 2018 Schedule:

Section

Meetings

Instructor

Comments

001

MWF	02:00pm	-	02:50pm
M	03:00pm	-	03:50pm

Cunningham, Gabriel

002

TuTh	11:00am	-	12:15pm
Tu	12:30pm	-	01:20pm

Eroshkin, Oleg


			Department of Mathematics University of Massachusetts Boston Phone: 617-287-6460; Fax: 617-287-6433 Information: math-info@math.umb.edu